Theorem nfna1 2151

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2156 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 2150	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1856	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1537  Ⅎwnf 1782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-10 2140

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1779  df-nf 1783

This theorem is referenced by:  dvelimhw  2346  nfeqf  2385  equs5  2464  sb4b  2479  nfsb2  2487  dvelimalcased  35090  dvelimexcased  35092  wl-equsb3  37558  wl-sbcom2d-lem1  37561  wl-euequf  37576  wl-ax11-lem3  37589  wl-ax11-lem4  37590  wl-ax11-lem6  37592  wl-ax11-lem7  37593