Theorem hbn1 2146

Description: Alias for ax-10 2145 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 2145	1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1535

This theorem was proved from axioms:  ax-10 2145

This theorem is referenced by:  hbe1  2147  hbe1a  2148  modal5  2159  axc7  2336  axc4  2340  axc14  2486  ax12indn  36081  axc5c4c711  40740  vk15.4j  40869  ax6e2nd  40899  ax6e2ndVD  41249  ax6e2ndALT  41271