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Theorem merlem4 1400
Description: Step 8 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
merlem4  |-  ( ta 
->  ( ( ta  ->  ph )  ->  ( th  ->  ph ) ) )

Proof of Theorem merlem4
StepHypRef Expression
1 ax-meredith 1396 . 2  |-  ( ( ( ( ( ph  ->  ph )  ->  ( -.  th  ->  -.  th )
)  ->  th )  ->  ta )  ->  (
( ta  ->  ph )  ->  ( th  ->  ph )
) )
2 merlem3 1399 . 2  |-  ( ( ( ( ( (
ph  ->  ph )  ->  ( -.  th  ->  -.  th )
)  ->  th )  ->  ta )  ->  (
( ta  ->  ph )  ->  ( th  ->  ph )
) )  ->  ( ta  ->  ( ( ta 
->  ph )  ->  ( th  ->  ph ) ) ) )
31, 2ax-mp 8 1  |-  ( ta 
->  ( ( ta  ->  ph )  ->  ( th  ->  ph ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  merlem5  1401  merlem6  1402  merlem7  1403  merlem12  1408  luk-2  1411
This theorem was proved from axioms:  ax-mp 8  ax-meredith 1396
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