Metamath Proof Explorer


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 ) )