Metamath Proof Explorer

Theorem frege57a

Description: Analogue of frege57aid . Proposition 57 of Frege1879 p. 51. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege57a ⊢ φ ↔ ψ → if- ψ χ θ → if- φ χ θ

Proof

Step Hyp Ref Expression
1 ax-frege52a ⊢ ψ ↔ φ → if- ψ χ θ → if- φ χ θ
2 frege56a ⊢ ψ ↔ φ → if- ψ χ θ → if- φ χ θ → φ ↔ ψ → if- ψ χ θ → if- φ χ θ
3 1 2 ax-mp ⊢ φ ↔ ψ → if- ψ χ θ → if- φ χ θ