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Theorem ax3 1547
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 1538 . 2  |-  ( ( -.  ph  ->  -.  ps )  ->  ( ( ( -.  ph  ->  ph )  ->  ph )  ->  ( ps  ->  ph ) ) )
2 luklem4 1540 . 2  |-  ( ( ( ( -.  ph  ->  ph )  ->  ph )  ->  ( ps  ->  ph )
)  ->  ( ps  ->  ph ) )
31, 2luklem1 1537 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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