Theorem hbn1 2138

Description: Alias for ax-10 2137 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

Step	Hyp	Ref	Expression
1		ax-10 2137	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1539

This theorem was proved from axioms:  ax-10 2137

This theorem is referenced by:  hbe1  2139  hbe1a  2140  modal5  2152  axc7  2310  axc4  2314  axc14  2461  ax12indn  37478  axc5c4c711  42803  vk15.4j  42932  ax6e2nd  42962  ax6e2ndVD  43312  ax6e2ndALT  43334