Theorem hbn1 2178

Description: Alias for ax-10 2177 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 2177	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1560

This theorem was proved from axioms:  ax-10 2177

This theorem is referenced by:  hbe1  2179  hbe1a  2180  modal5  2191  axc7  2351  axc4  2355  axc14  2496  ax12indn  39572  axc5c4c711  44982  vk15.4j  45109  ax6e2nd  45139  ax6e2ndVD  45488  ax6e2ndALT  45510