Theorem merco1lem4

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	merco1lem4	|- ( ( ( ph -> ps ) -> ch ) -> ( ps -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		merco1lem3	|- ( ( ( ( ps -> F. ) -> ( ph -> F. ) ) -> ( ( ch -> ph ) -> F. ) ) -> ( ( ch -> ph ) -> ( ps -> F. ) ) )
2		merco1	|- ( ( ( ( ( ps -> F. ) -> ( ph -> F. ) ) -> ( ( ch -> ph ) -> F. ) ) -> ( ( ch -> ph ) -> ( ps -> F. ) ) ) -> ( ( ( ( ch -> ph ) -> ( ps -> F. ) ) -> ps ) -> ( ph -> ps ) ) )
3	1 2	ax-mp	|- ( ( ( ( ch -> ph ) -> ( ps -> F. ) ) -> ps ) -> ( ph -> ps ) )
4		merco1	|- ( ( ( ( ( ch -> ph ) -> ( ps -> F. ) ) -> ps ) -> ( ph -> ps ) ) -> ( ( ( ph -> ps ) -> ch ) -> ( ps -> ch ) ) )
5	3 4	ax-mp	|- ( ( ( ph -> ps ) -> ch ) -> ( ps -> ch ) )