Theorem hbn1 2147

Description: Alias for ax-10 2146 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 2146	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1539

This theorem was proved from axioms:  ax-10 2146

This theorem is referenced by:  hbe1  2148  hbe1a  2149  modal5  2160  axc7  2322  axc4  2326  axc14  2467  ax12indn  39203  axc5c4c711  44642  vk15.4j  44769  ax6e2nd  44799  ax6e2ndVD  45148  ax6e2ndALT  45170