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Theorem hbn1 2060
Description: Alias for ax-10 2059 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 2059 1 (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1521
This theorem was proved from axioms:  ax-10 2059
This theorem is referenced by:  hbe1  2061  hbe1a  2062  modal-5  2072  axc4  2168  axc7  2170  axc14  2400  bj-modal5e  32761  ax12indn  34547  axc5c4c711  38919  vk15.4j  39051  ax6e2nd  39091  ax6e2ndVD  39458  ax6e2ndALT  39480
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