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Theorem hbn1 2139
Description: Alias for ax-10 2138 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 2138 1 (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1528
This theorem was proved from axioms:  ax-10 2138
This theorem is referenced by:  hbe1  2140  hbe1a  2141  modal5  2152  axc7  2330  axc4  2334  axc14  2483  ax12indn  35946  axc5c4c711  40594  vk15.4j  40723  ax6e2nd  40753  ax6e2ndVD  41103  ax6e2ndALT  41125
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