Theorem hbn1 2020

Description: Alias for ax-10 2019 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 2019	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1481

This theorem was proved from axioms:  ax-10 2019

This theorem is referenced by:  hbe1  2021  hbe1a  2022  modal-5  2032  axc4  2130  axc7  2132  axc14  2372  bj-modal5e  32636  ax12indn  34228  axc5c4c711  38602  vk15.4j  38734  ax6e2nd  38774  ax6e2ndVD  39144  ax6e2ndALT  39166