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Theorem a7s 1413
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 1407 . 2 (∀𝑦𝑥𝜑 → ∀𝑥𝑦𝜑)
2 a7s.1 . 2 (∀𝑥𝑦𝜑𝜓)
31, 2syl 14 1 (∀𝑦𝑥𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1312
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-7 1407
This theorem is referenced by:  cbv2h  1707  hbsb4t  1964  mor  2017
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