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Theorem ax3 1438
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 1429 . 2  |-  ( ( -.  ph  ->  -.  ps )  ->  ( ( ( -.  ph  ->  ph )  ->  ph )  ->  ( ps  ->  ph ) ) )
2 luklem4 1431 . 2  |-  ( ( ( ( -.  ph  ->  ph )  ->  ph )  ->  ( ps  ->  ph )
)  ->  ( ps  ->  ph ) )
31, 2luklem1 1428 1  |-  ( ( -.  ph  ->  -.  ps )  ->  ( ps  ->  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 8  ax-meredith 1411
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