Theorem hbn1 2139

Description: Alias for ax-10 2138 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 2138	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-10 2138

This theorem is referenced by:  hbe1  2140  hbe1a  2141  modal5  2153  axc7  2311  axc4  2315  axc14  2463  ax12indn  37813  axc5c4c711  43160  vk15.4j  43289  ax6e2nd  43319  ax6e2ndVD  43669  ax6e2ndALT  43691