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Theorem luklem3 1415
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 1412 . 2  |-  ( ph  ->  ( -.  ph  ->  -. 
th ) )
2 luklem2 1414 . 2  |-  ( ( -.  ph  ->  -.  th )  ->  ( ( ( -.  ph  ->  ps )  ->  ch )  ->  ( th  ->  ch ) ) )
31, 2luklem1 1413 1  |-  ( ph  ->  ( ( ( -. 
ph  ->  ps )  ->  ch )  ->  ( th 
->  ch ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  luklem4  1416  luklem5  1417
This theorem was proved from axioms:  ax-mp 8  ax-meredith 1396
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