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Theorem luklem1 1414
Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 23-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
luklem1.1  |-  ( ph  ->  ps )
luklem1.2  |-  ( ps 
->  ch )
Assertion
Ref Expression
luklem1  |-  ( ph  ->  ch )

Proof of Theorem luklem1
StepHypRef Expression
1 luklem1.2 . 2  |-  ( ps 
->  ch )
2 luklem1.1 . . 3  |-  ( ph  ->  ps )
3 luk-1 1411 . . 3  |-  ( (
ph  ->  ps )  -> 
( ( ps  ->  ch )  ->  ( ph  ->  ch ) ) )
42, 3ax-mp 10 . 2  |-  ( ( ps  ->  ch )  ->  ( ph  ->  ch ) )
51, 4ax-mp 10 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 6
This theorem is referenced by:  luklem2  1415  luklem3  1416  luklem4  1417  luklem5  1418  luklem6  1419  luklem7  1420  ax2  1423  ax3  1424
This theorem was proved from axioms:  ax-mp 10  ax-meredith 1397
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