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Theorem merlem6 1572
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 1570 . 2 |- ( ( ps -> ch ) -> ( ( ( ps -> ch ) -> ph ) -> ( th -> ph ) ) )
2 merlem3 1569 . 2 |- ( ( ( ps -> ch ) -> ( ( ( ps -> ch ) -> ph ) -> ( th -> ph ) ) ) -> ( ch -> ( ( ( ps -> ch ) -> ph ) -> ( th -> ph ) ) ) )
31, 2ax-mp 5 1 |- ( ch -> ( ( ( ps -> ch ) -> ph ) -> ( th -> ph ) ) )
Colors of variables: wff setvar class
Syntax hints:   -> 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:  merlem7  1573  merlem9  1575  merlem13  1579
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