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Theorem hbn1 2169
Description: Alias for ax-10 2168 to be used instead of it. (Contributed by NM, 24-Jan-1993.) (Proof shortened by Wolf Lammen, 18-Aug-2014.)
Assertion
Ref Expression
hbn1 (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

Proof of Theorem hbn1
StepHypRef Expression
1 ax-10 2168 1 (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1630
This theorem was proved from axioms:  ax-10 2168
This theorem is referenced by:  hbe1  2170  hbe1a  2171  modal-5  2181  axc4  2277  axc7  2279  axc14  2509  bj-modal5e  32964  ax12indn  34750  axc5c4c711  39122  vk15.4j  39254  ax6e2nd  39294  ax6e2ndVD  39661  ax6e2ndALT  39683
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