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Theorem ax3 1593
Description: Standard propositional axiom derived from Lukasiewicz axioms. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax3 |- ( ( -. ph -> -. ps ) -> ( ps -> ph ) )
Proof of Theorem ax3
StepHypRef Expression
1 luklem2 1584 . 2 |- ( ( -. ph -> -. ps ) -> ( ( ( -. ph -> ph ) -> ph ) -> ( ps -> ph ) ) )
2 luklem4 1586 . 2 |- ( ( ( ( -. ph -> ph ) -> ph ) -> ( ps -> ph ) ) -> ( ps -> ph ) )
31, 2luklem1 1583 1 |- ( ( -. ph -> -. ps ) -> ( ps -> ph ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by: (None)
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