Theorem merlem6

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.)

	Ref	Expression
Assertion	merlem6	|- ( ch -> ( ( ( ps -> ch ) -> ph ) -> ( th -> ph ) ) )

Proof

Step	Hyp	Ref	Expression
1		merlem4	|- ( ( ps -> ch ) -> ( ( ( ps -> ch ) -> ph ) -> ( th -> ph ) ) )
2		merlem3	|- ( ( ( ps -> ch ) -> ( ( ( ps -> ch ) -> ph ) -> ( th -> ph ) ) ) -> ( ch -> ( ( ( ps -> ch ) -> ph ) -> ( th -> ph ) ) ) )
3	1 2	ax-mp	|- ( ch -> ( ( ( ps -> ch ) -> ph ) -> ( th -> ph ) ) )