Theorem hbn1 2143

Description: Alias for ax-10 2142 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 2142	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1536

This theorem was proved from axioms:  ax-10 2142

This theorem is referenced by:  hbe1  2144  hbe1a  2145  modal5  2156  axc7  2325  axc4  2329  axc14  2475  ax12indn  36541  axc5c4c711  41500  vk15.4j  41629  ax6e2nd  41659  ax6e2ndVD  42009  ax6e2ndALT  42031