Metamath Proof Explorer

Theorem 19.33-2

Description: Theorem *11.421 in WhiteheadRussell p. 163. Theorem 19.33 of Margaris p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011)

Ref Expression
Assertion 19.33-2 ⊢ ∀ x ∀ y φ ∨ ∀ x ∀ y ψ → ∀ x ∀ y φ ∨ ψ

Proof

Step Hyp Ref Expression
1 orc ⊢ φ → φ ∨ ψ
2 1 2alimi ⊢ ∀ x ∀ y φ → ∀ x ∀ y φ ∨ ψ
3 olc ⊢ ψ → φ ∨ ψ
4 3 2alimi ⊢ ∀ x ∀ y ψ → ∀ x ∀ y φ ∨ ψ
5 2 4 jaoi ⊢ ∀ x ∀ y φ ∨ ∀ x ∀ y ψ → ∀ x ∀ y φ ∨ ψ