Theorem hbn1 2155

Description: Alias for ax-10 2154 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 2154	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1546

This theorem was proved from axioms:  ax-10 2154

This theorem is referenced by:  hbe1  2156  hbe1a  2157  modal5  2168  axc7  2328  axc4  2332  axc14  2473  ax12indn  39448  axc5c4c711  44858  vk15.4j  44985  ax6e2nd  45015  ax6e2ndVD  45364  ax6e2ndALT  45386