Metamath Proof Explorer


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 B
Assertion frege68c x φ ψ ψ [˙A / x]˙ φ

Proof

Step Hyp Ref Expression
1 frege59c.a A B
2 frege57aid x φ ψ ψ x φ
3 1 frege67c x φ ψ ψ x φ x φ ψ ψ [˙A / x]˙ φ
4 2 3 ax-mp x φ ψ ψ [˙A / x]˙ φ