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Theorem bj-hbalt 10290
Description: Closed form of hbal 1382 (copied from set.mm). (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-hbalt (∀𝑦(𝜑 → ∀𝑥𝜑) → (∀𝑦𝜑 → ∀𝑥𝑦𝜑))

Proof of Theorem bj-hbalt
StepHypRef Expression
1 alim 1362 . 2 (∀𝑦(𝜑 → ∀𝑥𝜑) → (∀𝑦𝜑 → ∀𝑦𝑥𝜑))
2 ax-7 1353 . 2 (∀𝑦𝑥𝜑 → ∀𝑥𝑦𝜑)
31, 2syl6 33 1 (∀𝑦(𝜑 → ∀𝑥𝜑) → (∀𝑦𝜑 → ∀𝑥𝑦𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1352  ax-7 1353
This theorem is referenced by:  bj-nfalt  10291
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