Theorem merlem2

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.)

	Ref	Expression
Assertion	merlem2	|- ( ( ( ph -> ph ) -> ch ) -> ( th -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		merlem1	|- ( ( ( ( ch -> ch ) -> ( -. ph -> -. th ) ) -> ph ) -> ( ph -> ph ) )
2		meredith	|- ( ( ( ( ( ch -> ch ) -> ( -. ph -> -. th ) ) -> ph ) -> ( ph -> ph ) ) -> ( ( ( ph -> ph ) -> ch ) -> ( th -> ch ) ) )
3	1 2	ax-mp	|- ( ( ( ph -> ph ) -> ch ) -> ( th -> ch ) )