Theorem frege61c

Description: Lemma for frege65c . Proposition 61 of Frege1879 p. 52. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	frege59c.a	|- A e. B
Assertion	frege61c	|- ( ( [. A / x ]. ph -> ps ) -> ( A. x ph -> ps ) )

Proof

Step	Hyp	Ref	Expression
1		frege59c.a	|- A e. B
2	1	frege58c	|- ( A. x ph -> [. A / x ]. ph )
3		frege9	|- ( ( A. x ph -> [. A / x ]. ph ) -> ( ( [. A / x ]. ph -> ps ) -> ( A. x ph -> ps ) ) )
4	2 3	ax-mp	|- ( ( [. A / x ]. ph -> ps ) -> ( A. x ph -> ps ) )