Theorem 2ax5 1937

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

Assertion

Ref	Expression
2ax5	⊢ (𝜑 → ∀𝑥∀𝑦𝜑)

Distinct variable groups:   𝜑,𝑥   𝜑,𝑦

Proof of Theorem 2ax5

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝜑 → 𝜑)
2	1	alrimivv 1928	1 ⊢ (𝜑 → ∀𝑥∀𝑦𝜑)

Syntax hints:   → wi 4  ∀wal 1538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1795  ax-4 1809  ax-5 1910

This theorem is referenced by:  iscnrm3lem2  48832