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