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Theorem luklem3 1585
Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
luklem3 |- ( ph -> ( ( ( -. ph -> ps ) -> ch ) -> ( th -> ch ) ) )
Proof of Theorem luklem3
StepHypRef Expression
1 luk-3 1582 . 2 |- ( ph -> ( -. ph -> -. th ) )
2 luklem2 1584 . 2 |- ( ( -. ph -> -. th ) -> ( ( ( -. ph -> ps ) -> ch ) -> ( th -> ch ) ) )
31, 2luklem1 1583 1 |- ( ph -> ( ( ( -. ph -> ps ) -> ch ) -> ( th -> ch ) ) )
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:  luklem4  1586  luklem5  1587
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