Theorem hbn1 2179

Description: Alias for ax-10 2178 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 2178	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4  ∀wal 1568

This proof depends on axioms:  ax-10 2178

This theorem is used by:  hbe1  2180  hbe1a  2181  modal5  2192  axc7  2349  axc4  2353  axc14  2494  ax12indn  39803  axc5c4c711  45212  vk15.4j  45338  ax6e2nd  45368  ax6e2ndVD  45717  ax6e2ndALT  45739