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Theorem merlem2 1568
Description: Step 4 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
merlem2 |- ( ( ( ph -> ph ) -> ch ) -> ( th -> ch ) )
Proof of Theorem merlem2
StepHypRef Expression
1 merlem1 1567 . 2 |- ( ( ( ( ch -> ch ) -> ( -. ph -> -. th ) ) -> ph ) -> ( ph -> ph ) )
2 meredith 1566 . 2 |- ( ( ( ( ( ch -> ch ) -> ( -. ph -> -. th ) ) -> ph ) -> ( ph -> ph ) ) -> ( ( ( ph -> ph ) -> ch ) -> ( th -> ch ) ) )
31, 2ax-mp 5 1 |- ( ( ( ph -> ph ) -> ch ) -> ( th -> ch ) )
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:  merlem3  1569  merlem12  1578
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