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 x φ ψ ψ y x φ

Proof

Step Hyp Ref Expression
1 frege57aid x φ ψ ψ x φ
2 frege67b x φ ψ ψ x φ x φ ψ ψ y x φ
3 1 2 ax-mp x φ ψ ψ y x φ