Theorem nfna1 2165

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2170 in conjunction with distinctors. (Contributed by Wolf Lammen, 2-Sep-2018.)

Assertion

Ref	Expression
nfna1	⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Proof of Theorem nfna1

Step	Hyp	Ref	Expression
1		nfa1 2164	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1865	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1546  Ⅎwnf 1791

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-10 2154

This theorem depends on definitions:  df-bi 209  df-or 855  df-ex 1788  df-nf 1792

This theorem is referenced by:  dvelimhw  2355  nfeqf  2391  equs5  2470  sb4b  2485  nfsb2  2493  dvelimalcased  35270  dvelimexcased  35272  regsfromsetind  36780  wl-equsb3  37940  wl-sbcom2d-lem1  37943  wl-euequf  37958