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Theorem merlem8 1574
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 meredith 1566 . 2 |- ( ( ( ( ( ph -> ph ) -> ( -. ph -> -. ph ) ) -> ph ) -> ph ) -> ( ( ph -> ph ) -> ( ph -> ph ) ) )
2 merlem7 1573 . 2 |- ( ( ( ( ( ( ph -> ph ) -> ( -. ph -> -. ph ) ) -> ph ) -> ph ) -> ( ( ph -> ph ) -> ( ph -> ph ) ) ) -> ( ( ( ps -> ch ) -> th ) -> ( ( ( ch -> ta ) -> ( -. th -> -. ps ) ) -> th ) ) )
31, 2ax-mp 5 1 |- ( ( ( ps -> ch ) -> th ) -> ( ( ( ch -> ta ) -> ( -. th -> -. ps ) ) -> th ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  merlem9  1575
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