Theorem merco1lem5

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	merco1lem5	|- ( ( ( ( ph -> F. ) -> ch ) -> ta ) -> ( ph -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		merco1lem4	|- ( ( ( ( ta -> ph ) -> ( ph -> F. ) ) -> ch ) -> ( ( ph -> F. ) -> ch ) )
2		merco1	|- ( ( ( ( ( ta -> ph ) -> ( ph -> F. ) ) -> ch ) -> ( ( ph -> F. ) -> ch ) ) -> ( ( ( ( ph -> F. ) -> ch ) -> ta ) -> ( ph -> ta ) ) )
3	1 2	ax-mp	|- ( ( ( ( ph -> F. ) -> ch ) -> ta ) -> ( ph -> ta ) )