Theorem merco1lem16

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 . (Contributed by Anthony Hart, 18-Sep-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	merco1lem16	|- ( ( ( ph -> ( ps -> ch ) ) -> ta ) -> ( ( ph -> ch ) -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		merco1lem15	|- ( ( ph -> ch ) -> ( ph -> ( ps -> ch ) ) )
2		merco1lem11	|- ( ( ( ph -> ch ) -> ( ph -> ( ps -> ch ) ) ) -> ( ( ( ( ta -> ph ) -> ( ( ph -> ch ) -> F. ) ) -> F. ) -> ( ph -> ( ps -> ch ) ) ) )
3	1 2	ax-mp	|- ( ( ( ( ta -> ph ) -> ( ( ph -> ch ) -> F. ) ) -> F. ) -> ( ph -> ( ps -> ch ) ) )
4		merco1	|- ( ( ( ( ( ta -> ph ) -> ( ( ph -> ch ) -> F. ) ) -> F. ) -> ( ph -> ( ps -> ch ) ) ) -> ( ( ( ph -> ( ps -> ch ) ) -> ta ) -> ( ( ph -> ch ) -> ta ) ) )
5	3 4	ax-mp	|- ( ( ( ph -> ( ps -> ch ) ) -> ta ) -> ( ( ph -> ch ) -> ta ) )