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Theorem bj-hbalt 34072
Description: Closed form of hbal 2175. When in main part, prove hbal 2175 and hbald 2176 from it. (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 1812 . 2 (∀𝑦(𝜑 → ∀𝑥𝜑) → (∀𝑦𝜑 → ∀𝑦𝑥𝜑))
2 ax-11 2162 . 2 (∀𝑦𝑥𝜑 → ∀𝑥𝑦𝜑)
31, 2syl6 35 1 (∀𝑦(𝜑 → ∀𝑥𝜑) → (∀𝑦𝜑 → ∀𝑥𝑦𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1811  ax-11 2162
This theorem is referenced by:  bj-hbext  34101  bj-nfalt  34102  bj-cbv3ta  34167
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