Metamath Proof Explorer

Theorem 19.31vv

Description: Theorem *11.44 in WhiteheadRussell p. 163. Theorem 19.31 of Margaris p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011)

Ref Expression
Assertion 19.31vv ⊢ ∀ x ∀ y φ ∨ ψ ↔ ∀ x ∀ y φ ∨ ψ

Proof

Step Hyp Ref Expression
1 19.31v ⊢ ∀ y φ ∨ ψ ↔ ∀ y φ ∨ ψ
2 1 albii ⊢ ∀ x ∀ y φ ∨ ψ ↔ ∀ x ∀ y φ ∨ ψ
3 19.31v ⊢ ∀ x ∀ y φ ∨ ψ ↔ ∀ x ∀ y φ ∨ ψ
4 2 3 bitri ⊢ ∀ x ∀ y φ ∨ ψ ↔ ∀ x ∀ y φ ∨ ψ