Theorem hbn1 2131

Description: Alias for ax-10 2130 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 2130	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1532

This theorem was proved from axioms:  ax-10 2130

This theorem is referenced by:  hbe1  2132  hbe1a  2133  modal5  2145  axc7  2306  axc4  2310  axc14  2457  ax12indn  38652  axc5c4c711  44110  vk15.4j  44239  ax6e2nd  44269  ax6e2ndVD  44619  ax6e2ndALT  44641