Metamath Proof Explorer

Theorem frege68a

Description: Combination of applying a definition and applying it to a specific instance. Proposition 68 of Frege1879 p. 54. (Contributed by RP, 17-Apr-2020) (Proof modification is discouraged.)

Ref Expression
Assertion frege68a ⊢ ψ ∧ χ ↔ θ → θ → if- φ ψ χ

Proof

Step Hyp Ref Expression
1 frege57aid ⊢ ψ ∧ χ ↔ θ → θ → ψ ∧ χ
2 frege67a ⊢ ψ ∧ χ ↔ θ → θ → ψ ∧ χ → ψ ∧ χ ↔ θ → θ → if- φ ψ χ
3 1 2 ax-mp ⊢ ψ ∧ χ ↔ θ → θ → if- φ ψ χ