Theorem a7s 689

Description: Swap quantifiers in an antecedent.

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-7 676	. 2 ⊢ (∀y∀xφ → ∀x∀yφ)
2		a7s.1	. 2 ⊢ (∀x∀yφ → ψ)
3	1, 2	syl 12	1 ⊢ (∀y∀xφ → ψ)

Syntax hints:   → wi 2  ∀wal 672

This theorem is referenced by:  cbv1 845  cbv2 846  hbsb4 905  hbsb4t 906  sb9i 920  mo 1020

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6  ax-7 676

metamath.org