Theorem hbn1 2186

Description: Alias for ax-10 2185 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 2185	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1651

This theorem was proved from axioms:  ax-10 2185

This theorem is referenced by:  hbe1  2187  hbe1a  2188  modal5  2199  axc7  2339  axc4  2343  axc14  2489  ax12indn  34964  axc5c4c711  39383  vk15.4j  39514  ax6e2nd  39544  ax6e2ndVD  39904  ax6e2ndALT  39926