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Theorem a7s 1386
Description: Swap quantifiers in an antecedent. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
a7s.1 (∀𝑥𝑦𝜑𝜓)
Assertion
Ref Expression
a7s (∀𝑦𝑥𝜑𝜓)

Proof of Theorem a7s
StepHypRef Expression
1 ax-7 1380 . 2 (∀𝑦𝑥𝜑 → ∀𝑥𝑦𝜑)
2 a7s.1 . 2 (∀𝑥𝑦𝜑𝜓)
31, 2syl 14 1 (∀𝑦𝑥𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-7 1380
This theorem is referenced by:  cbv2h  1678  hbsb4t  1934  mor  1987
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