Metamath Proof Explorer


Theorem 2ax5

Description: Quantification of two variables over a formula in which they do not occur. (Contributed by Alan Sare, 12-Apr-2011)

Ref Expression
Assertion 2ax5 ⊢ φ → ∀ x ∀ y φ

Proof

Step Hyp Ref Expression
1 id ⊢ φ → φ
2 1 alrimivv ⊢ φ → ∀ x ∀ y φ