Theorem frege68b

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
Assertion	frege68b	|- ( ( A. x ph <-> ps ) -> ( ps -> [ y / x ] ph ) )

Proof

Step	Hyp	Ref	Expression
1		frege57aid	|- ( ( A. x ph <-> ps ) -> ( ps -> A. x ph ) )
2		frege67b	|- ( ( ( A. x ph <-> ps ) -> ( ps -> A. x ph ) ) -> ( ( A. x ph <-> ps ) -> ( ps -> [ y / x ] ph ) ) )
3	1 2	ax-mp	|- ( ( A. x ph <-> ps ) -> ( ps -> [ y / x ] ph ) )