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Theorem luk-3 1412
Description: 3 of 3 axioms for propositional calculus due to Lukasiewicz, derived from Meredith's sole axiom. (Contributed by NM, 14-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
luk-3  |-  ( ph  ->  ( -.  ph  ->  ps ) )

Proof of Theorem luk-3
StepHypRef Expression
1 merlem11 1407 . 2  |-  ( ( -.  ph  ->  ( -. 
ph  ->  ps ) )  ->  ( -.  ph  ->  ps ) )
2 merlem1 1397 . 2  |-  ( ( ( -.  ph  ->  ( -.  ph  ->  ps )
)  ->  ( -.  ph 
->  ps ) )  -> 
( ph  ->  ( -. 
ph  ->  ps ) ) )
31, 2ax-mp 8 1  |-  ( ph  ->  ( -.  ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  luklem2  1414  luklem3  1415
This theorem was proved from axioms:  ax-mp 8  ax-meredith 1396
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