Theorem hbn1 2181

Description: Alias for ax-10 2180 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 2180	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4  ∀wal 1568

This proof depends on axioms:  ax-10 2180

This theorem is used by:  hbe1  2182  hbe1a  2183  modal5  2195  axc7  2351  axc4  2355  axc14  2495  ax12indn  40191  axc5c4c711  45575  vk15.4j  45700  ax6e2nd  45730  ax6e2ndVD  46079  ax6e2ndALT  46101