Metamath Proof Explorer

Theorem frege62b

Description: A kind of Aristotelian inference. This judgement replaces the mode of inference barbara when the minor premise has a particular context. Proposition 62 of Frege1879 p. 52. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege62b ⊢ y x φ → ∀ x φ → ψ → y x ψ

Proof

Step Hyp Ref Expression
1 frege58bcor ⊢ ∀ x φ → ψ → y x φ → y x ψ
2 ax-frege8 ⊢ ∀ x φ → ψ → y x φ → y x ψ → y x φ → ∀ x φ → ψ → y x ψ
3 1 2 ax-mp ⊢ y x φ → ∀ x φ → ψ → y x ψ