https://www.vigyanwiki.in/index.php?action=history&feed=atom&title=Template%3ATransformation_rules
Template:Transformation rules - Revision history
2026-06-27T10:55:10Z
Revision history for this page on the wiki
MediaWiki 1.39.3
https://www.vigyanwiki.in/index.php?title=Template:Transformation_rules&diff=94148&oldid=prev
Indicwiki: 1 revision imported from :alpha:Template:Transformation_rules
2023-02-22T16:24:47Z
<p>1 revision imported from <a href="https://alpha.indicwiki.in/index.php?title=Template:Transformation_rules" class="extiw" title="alpha:Template:Transformation rules">alpha:Template:Transformation_rules</a></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<tr class="diff-title" lang="en-GB">
<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:54, 22 February 2023</td>
</tr><tr><td colspan="2" class="diff-notice" lang="en-GB"><div class="mw-diff-empty">(No difference)</div>
</td></tr></table>
Indicwiki
https://www.vigyanwiki.in/index.php?title=Template:Transformation_rules&diff=94147&oldid=prev
alpha>Indicwiki: Created page with "{{Sidebar | class = plainlist | title = Transformation rules | headingstyle = background:#eaeaff; | contentstyle = padding-top:0.15em; | heading1..."
2023-02-13T06:49:21Z
<p>Created page with "{{Sidebar | class = plainlist | title = <a href="/index.php?title=Rule_of_inference&action=edit&redlink=1" class="new" title="Rule of inference (page does not exist)">Transformation rules</a> | headingstyle = background:#eaeaff; | contentstyle = padding-top:0.15em; | heading1..."</p>
<p><b>New page</b></p><div>{{Sidebar<br />
| class = plainlist<br />
| title = [[Rule of inference|Transformation rules]]<br />
<br />
| headingstyle = background:#eaeaff;<br />
| contentstyle = padding-top:0.15em;<br />
<br />
| heading1style = background:#ddf;font-size:110%; border-bottom:1px #fefefe solid;<br />
| heading1 = [[Propositional calculus]]<br />
<br />
| heading2 = [[Rule of inference|Rules of inference]]<br />
| content2 =<br />
* [[Conditional proof|<span>Implication introduction</span>]]{{\}}<!--<br />
-->[[Modus ponens|<span title="A→B, &nbsp; A &nbsp; ⊢ &nbsp; B">elimination (''modus ponens'')</span>]]<br />
* [[Biconditional introduction|<span title="A→B, &nbsp; B→A &nbsp; ⊢ &nbsp; A↔B">Biconditional introduction</span>]]{{\}}<!--<br />
-->[[Biconditional elimination|<span title="A↔B &nbsp; ⊢ &nbsp; A→B"><!--Biconditional -->elimination</span>]]<br />
* [[Conjunction introduction|<span title="A, &nbsp; B &nbsp; ⊢ &nbsp; A∧B">Conjunction introduction</span>]]{{\}}<!--<br />
-->[[Conjunction elimination|<span title="A∧B &nbsp; ⊢ &nbsp; A">elimination</span>]]<br />
* [[Disjunction introduction|<span title="A &nbsp; ⊢ &nbsp; A∨B">Disjunction introduction</span>]]{{\}}<!--<br />
-->[[Disjunction elimination|<span title="A∨B, &nbsp; A→C, &nbsp; B→C &nbsp; ⊢ &nbsp; C"><!--Disjunction -->elimination</span>]]<br />
* [[Disjunctive syllogism|<span title="A∨B, &nbsp; ¬A &nbsp; ⊢ &nbsp; B">Disjunctive<!-- syllogism--></span>]]{{\}}<!--<br />
-->[[Hypothetical syllogism|<span title="A→B, &nbsp; B→C &nbsp; ⊢ &nbsp; A→C">hypothetical syllogism</span>]]<br />
* [[Constructive dilemma|<span title="A→P, &nbsp; B→Q, &nbsp; A∨B &nbsp; ⊢ &nbsp; P∨Q">Constructive<!-- dilemma--></span>]]{{\}}<!--<br />
-->[[Destructive dilemma|<span title="A→P, &nbsp; B→Q, &nbsp; ¬P∨¬Q &nbsp; ⊢ &nbsp; ¬A∨¬B">destructive dilemma</span>]]<br />
* [[Absorption (logic)|<span title="A→B &nbsp; ⊢ &nbsp; A→A∧B">Absorption</span>]]{{\}}<!--<br />
-->[[Modus tollens|<span title="A→B, &nbsp; ¬B &nbsp; ⊢ &nbsp; ¬A">''modus tollens''</span>]]{{\}}<!--<br />
-->[[Modus ponendo tollens|<span title="¬(A∧B), &nbsp; A &nbsp; ⊢ &nbsp; ¬B">''modus ponendo tollens''</span>]]<br />
* [[Negation introduction]]<br />
| heading3 = [[Rule of replacement|Rules of replacement]]<br />
| content3 = {{startflatlist}}<br />
* [[Associative property#Propositional logic|<span title="A∨(B∨C) &nbsp; = &nbsp; (A∨B)∨C">Associativity</span>]]<br />
* [[Commutative property#Propositional logic|<span title="A∨B &nbsp; = &nbsp; B∨A">Commutativity</span>]]<br />
* [[Distributive property#Propositional logic|<span title="A∧(B∨C) &nbsp; = &nbsp; (A∧B)∨(A∧C)">Distributivity</span>]]<br />
* [[Double negation|<span title="¬¬A &nbsp; = &nbsp; A">Double negation</span>]]<br />
* [[De Morgan's laws]]<br />
* [[Transposition (logic)|Transposition]]<br />
* [[Material implication (rule of inference)|<span title="A→B &nbsp; ⊢ &nbsp; ¬A∨B">Material implication</span>]]<br />
* [[Exportation (logic)|<span title="(A∧B)→C &nbsp; ⊢ &nbsp; A→(B→C)">Exportation</span>]]<br />
* [[Tautology (rule of inference)|<span title="A∨A &nbsp; = &nbsp; A">Tautology</span>]]<br />
{{endflatlist}}<br />
<br />
| heading4style = background:#ddf;font-size:110%;<br />
| heading4 = [[First-order logic|Predicate logic]]<br />
| heading5 = [[Rule of inference|Rules of inference]]<br />
| content5 =<br />
* [[Universal generalization]]{{\}}[[Universal instantiation|instantiation]]<br />
* [[Existential generalization]]{{\}}[[Existential instantiation|instantiation]]<br />
<br />
}}<noinclude>{{doc|content=<br />
<br />
===See also===<br />
* {{tl|Classical logic}}<br />
* {{tl|Logic templates}}<br />
<br />
[[Category:Logic templates]]<br />
[[Category:Mathematics sidebar templates]]<br />
[[Category:Philosophy and thinking sidebar templates]]<br />
}}</noinclude></div>
alpha>Indicwiki