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Theorem peirce 181
 Description: Peirce's axiom. This odd-looking theorem is the "difference" between an intuitionistic system of propositional calculus and a classical system and is not accepted by intuitionists. When Peirce's axiom is added to an intuitionistic system, the system becomes equivalent to our classical system ax-1 6 through ax-3 8. A curious fact about this theorem is that it requires ax-3 8 for its proof even though the result has no negation connectives in it. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 9-Oct-2012.)
Assertion
Ref Expression
peirce

Proof of Theorem peirce
StepHypRef Expression
1 simplim 151 . 2
2 id 22 . 2
31, 2ja 161 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4 This theorem is referenced by:  looinv  182  tbw-ax3  1535  tb-ax3  29846  bj-peircei  34145 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
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