Theorem a7s 1447

Description: Swap quantifiers in an antecedent. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
a7s.1	⊢ (∀𝑥∀𝑦𝜑 → 𝜓)

Assertion

Ref	Expression
a7s	⊢ (∀𝑦∀𝑥𝜑 → 𝜓)

Proof of Theorem a7s

Step	Hyp	Ref	Expression
1		ax-7 1441	. 2 ⊢ (∀𝑦∀𝑥𝜑 → ∀𝑥∀𝑦𝜑)
2		a7s.1	. 2 ⊢ (∀𝑥∀𝑦𝜑 → 𝜓)
3	1, 2	syl 14	1 ⊢ (∀𝑦∀𝑥𝜑 → 𝜓)

Syntax hints:   → wi 4  ∀wal 1346

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-7 1441

This theorem is referenced by:  cbv2h  1741  hbsb4t  2006  mor  2061