Theorem hbn1 2176

Description: Alias for ax-10 2175 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 2175	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

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

This proof depends on axioms:  ax-10 2175

This theorem is used by:  hbe1  2177  hbe1a  2178  modal5  2189  axc7  2349  axc4  2353  axc14  2494  ax12indn  39745  axc5c4c711  45139  vk15.4j  45265  ax6e2nd  45295  ax6e2ndVD  45644  ax6e2ndALT  45666