Theorem 2ax5 1969

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 23	. 2 ⊢ (𝜑 → 𝜑)
2	1	alrimivv 1960	1 ⊢ (𝜑 → ∀𝑥∀𝑦𝜑)

This proof depends on syntax axioms:   → wi 4  ∀wal 1567

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1827  ax-4 1841  ax-5 1942

This theorem is used by:  iscnrm3lem2  50043