Theorem a7s 988

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-7 959	. 2 ⊢ (∀y∀xφ → ∀x∀yφ)
2		a7s.1	. 2 ⊢ (∀x∀yφ → ψ)
3	1, 2	syl 10	1 ⊢ (∀y∀xφ → ψ)

Syntax hints:   → wi 3  ∀wal 951

This theorem is referenced by:  cbv1 1158  cbv2 1159  hbsb4 1243  hbsb4t 1244  sb9i 1258  mo 1386  hbfvd2 3716

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7  ax-7 959

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