Theorem a7s 1340

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 1334	. 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 1240

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-7 1334

This theorem is referenced by:  cbv2h  1631  hbsb4t  1886  mor  1939