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)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4  ∀wal 1567

This proof depends on axioms:  ax-10 2177

This theorem is used by:  hbe1  2179  hbe1a  2180  modal5  2191  axc7  2347  axc4  2351  axc14  2492  ax12indn  40001  axc5c4c711  45385  vk15.4j  45511  ax6e2nd  45541  ax6e2ndVD  45890  ax6e2ndALT  45912