Theorem a7s 1735

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 1734	. 2 ⊢ (∀y∀xφ → ∀x∀yφ)
2		a7s.1	. 2 ⊢ (∀x∀yφ → ψ)
3	1, 2	syl 15	1 ⊢ (∀y∀xφ → ψ)

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-7 1734

This theorem is referenced by:  cbv3hv  1850  cbv3hvOLD  1851  cbv1h  1978  cbv2h  1980  sb9i  2094  ax10-16  2190