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Theorem hbaltg 30759
Description: A more general and closed form of hbal 2021. (Contributed by Scott Fenton, 13-Dec-2010.)
Assertion
Ref Expression
hbaltg (∀𝑥(𝜑 → ∀𝑦𝜓) → (∀𝑥𝜑 → ∀𝑦𝑥𝜓))

Proof of Theorem hbaltg
StepHypRef Expression
1 alim 1727 . 2 (∀𝑥(𝜑 → ∀𝑦𝜓) → (∀𝑥𝜑 → ∀𝑥𝑦𝜓))
2 ax-11 2019 . 2 (∀𝑥𝑦𝜓 → ∀𝑦𝑥𝜓)
31, 2syl6 34 1 (∀𝑥(𝜑 → ∀𝑦𝜓) → (∀𝑥𝜑 → ∀𝑦𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1726  ax-11 2019
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator