Theorem hbn1 2138

Description: Alias for ax-10 2137 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 2137	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1537

This theorem was proved from axioms:  ax-10 2137

This theorem is referenced by:  hbe1  2139  hbe1a  2140  modal5  2152  axc7  2311  axc4  2315  axc14  2463  ax12indn  36957  axc5c4c711  42019  vk15.4j  42148  ax6e2nd  42178  ax6e2ndVD  42528  ax6e2ndALT  42550