Metamath Proof Explorer

Theorem frege66b

Description: Swap antecedents of frege65b . Proposition 66 of Frege1879 p. 54. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege66b ⊢ ∀ x φ → ψ → ∀ x χ → φ → y x χ → y x ψ

Proof

Step Hyp Ref Expression
1 frege65b ⊢ ∀ x χ → φ → ∀ x φ → ψ → y x χ → y x ψ
2 ax-frege8 ⊢ ∀ x χ → φ → ∀ x φ → ψ → y x χ → y x ψ → ∀ x φ → ψ → ∀ x χ → φ → y x χ → y x ψ
3 1 2 ax-mp ⊢ ∀ x φ → ψ → ∀ x χ → φ → y x χ → y x ψ