Metamath Proof Explorer

Theorem 19.21vv

Description: Compare Theorem *11.3 in WhiteheadRussell p. 161. Special case of theorem 19.21 of Margaris p. 90 with two quantifiers. See 19.21v . (Contributed by Andrew Salmon, 24-May-2011)

Ref Expression
Assertion 19.21vv ⊢ ∀ x ∀ y ψ → φ ↔ ψ → ∀ x ∀ y φ

Proof

Step Hyp Ref Expression
1 19.21v ⊢ ∀ y ψ → φ ↔ ψ → ∀ y φ
2 1 albii ⊢ ∀ x ∀ y ψ → φ ↔ ∀ x ψ → ∀ y φ
3 19.21v ⊢ ∀ x ψ → ∀ y φ ↔ ψ → ∀ x ∀ y φ
4 2 3 bitri ⊢ ∀ x ∀ y ψ → φ ↔ ψ → ∀ x ∀ y φ