Metamath Proof Explorer

Theorem pm11.12

Description: Theorem *11.12 in WhiteheadRussell p. 159. (Contributed by Andrew Salmon, 17-Jun-2011)

Ref Expression
Assertion pm11.12 ⊢ ∀ x ∀ y φ ∨ ψ → φ ∨ ∀ x ∀ y ψ

Proof

Step Hyp Ref Expression
1 pm10.12 ⊢ ∀ y φ ∨ ψ → φ ∨ ∀ y ψ
2 1 alimi ⊢ ∀ x ∀ y φ ∨ ψ → ∀ x φ ∨ ∀ y ψ
3 pm10.12 ⊢ ∀ x φ ∨ ∀ y ψ → φ ∨ ∀ x ∀ y ψ
4 2 3 syl ⊢ ∀ x ∀ y φ ∨ ψ → φ ∨ ∀ x ∀ y ψ