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Theorem merlem6 1402
Description: Step 12 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 14-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merlem6  |-  ( ch 
->  ( ( ( ps 
->  ch )  ->  ph )  ->  ( th  ->  ph )
) )

Proof of Theorem merlem6
StepHypRef Expression
1 merlem4 1400 . 2  |-  ( ( ps  ->  ch )  ->  ( ( ( ps 
->  ch )  ->  ph )  ->  ( th  ->  ph )
) )
2 merlem3 1399 . 2  |-  ( ( ( ps  ->  ch )  ->  ( ( ( ps  ->  ch )  ->  ph )  ->  ( th  ->  ph ) ) )  ->  ( ch  ->  ( ( ( ps  ->  ch )  ->  ph )  -> 
( th  ->  ph )
) ) )
31, 2ax-mp 8 1  |-  ( ch 
->  ( ( ( ps 
->  ch )  ->  ph )  ->  ( th  ->  ph )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  merlem7  1403  merlem9  1405  merlem13  1409
This theorem was proved from axioms:  ax-mp 8  ax-meredith 1396
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