Theorem nfna1 2185

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2190 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 2184	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1885	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1566  Ⅎwnf 1811

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-10 2174

This theorem depends on definitions:  df-bi 210  df-or 861  df-ex 1808  df-nf 1812

This theorem is referenced by:  dvelimhw  2375  nfeqf  2411  equs5  2490  sb4b  2505  nfsb2  2513  dvelimalcased  35429  dvelimexcased  35431  regsfromsetind  36994  wl-equsb3  38155  wl-sbcom2d-lem1  38158  wl-euequf  38173