Theorem frege68c

Description: Combination of applying a definition and applying it to a specific instance. Proposition 68 of Frege1879 p. 54. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	frege59c.a	|- A e. B
Assertion	frege68c	|- ( ( A. x ph <-> ps ) -> ( ps -> [. A / x ]. ph ) )

Proof

Step	Hyp	Ref	Expression
1		frege59c.a	|- A e. B
2		frege57aid	|- ( ( A. x ph <-> ps ) -> ( ps -> A. x ph ) )
3	1	frege67c	|- ( ( ( A. x ph <-> ps ) -> ( ps -> A. x ph ) ) -> ( ( A. x ph <-> ps ) -> ( ps -> [. A / x ]. ph ) ) )
4	2 3	ax-mp	|- ( ( A. x ph <-> ps ) -> ( ps -> [. A / x ]. ph ) )