Theorem nfna1 2188

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2193 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 2187	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1879	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1560  Ⅎwnf 1805

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-10 2177

This theorem depends on definitions:  df-bi 209  df-or 859  df-ex 1802  df-nf 1806

This theorem is referenced by:  dvelimhw  2378  nfeqf  2414  equs5  2493  sb4b  2508  nfsb2  2516  dvelimalcased  35372  dvelimexcased  35374  regsfromsetind  36904  wl-equsb3  38064  wl-sbcom2d-lem1  38067  wl-euequf  38082