Theorem merco1lem8

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 . (Contributed by Anthony Hart, 17-Sep-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	merco1lem8	|- ( ph -> ( ( ps -> ( ps -> ch ) ) -> ( ps -> ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		merco1lem6	|- ( ( ps -> ( ps -> ch ) ) -> ( ( ps -> ( ps -> ch ) ) -> ( ps -> ch ) ) )
2		merco1lem6	|- ( ( ( ps -> ( ps -> ch ) ) -> ( ( ps -> ( ps -> ch ) ) -> ( ps -> ch ) ) ) -> ( ph -> ( ( ps -> ( ps -> ch ) ) -> ( ps -> ch ) ) ) )
3	1 2	ax-mp	|- ( ph -> ( ( ps -> ( ps -> ch ) ) -> ( ps -> ch ) ) )