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Theorem merlem8 1404
Description: Step 15 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merlem8  |-  ( ( ( ps  ->  ch )  ->  th )  ->  (
( ( ch  ->  ta )  ->  ( -.  th 
->  -.  ps ) )  ->  th ) )

Proof of Theorem merlem8
StepHypRef Expression
1 ax-meredith 1396 . 2  |-  ( ( ( ( ( ph  ->  ph )  ->  ( -.  ph  ->  -.  ph )
)  ->  ph )  ->  ph )  ->  ( (
ph  ->  ph )  ->  ( ph  ->  ph ) ) )
2 merlem7 1403 . 2  |-  ( ( ( ( ( (
ph  ->  ph )  ->  ( -.  ph  ->  -.  ph )
)  ->  ph )  ->  ph )  ->  ( (
ph  ->  ph )  ->  ( ph  ->  ph ) ) )  ->  ( ( ( ps  ->  ch )  ->  th )  ->  (
( ( ch  ->  ta )  ->  ( -.  th 
->  -.  ps ) )  ->  th ) ) )
31, 2ax-mp 8 1  |-  ( ( ( ps  ->  ch )  ->  th )  ->  (
( ( ch  ->  ta )  ->  ( -.  th 
->  -.  ps ) )  ->  th ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  merlem9  1405
This theorem was proved from axioms:  ax-mp 8  ax-meredith 1396
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