Metamath Proof Explorer

Theorem 2albi

Description: Theorem *11.33 in WhiteheadRussell p. 162. Theorem 19.15 of Margaris p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011)

Ref Expression
Assertion 2albi ⊢ ∀ x ∀ y φ ↔ ψ → ∀ x ∀ y φ ↔ ∀ x ∀ y ψ

Proof

Step Hyp Ref Expression
1 albi ⊢ ∀ y φ ↔ ψ → ∀ y φ ↔ ∀ y ψ
2 1 alimi ⊢ ∀ x ∀ y φ ↔ ψ → ∀ x ∀ y φ ↔ ∀ y ψ
3 albi ⊢ ∀ x ∀ y φ ↔ ∀ y ψ → ∀ x ∀ y φ ↔ ∀ x ∀ y ψ
4 2 3 syl ⊢ ∀ x ∀ y φ ↔ ψ → ∀ x ∀ y φ ↔ ∀ x ∀ y ψ