Theorem nfna1 2163

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2168 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 2162	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1864	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1545  Ⅎwnf 1790

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-10 2152

This theorem depends on definitions:  df-bi 208  df-or 854  df-ex 1787  df-nf 1791

This theorem is referenced by:  dvelimhw  2353  nfeqf  2389  equs5  2468  sb4b  2483  nfsb2  2491  dvelimalcased  35257  dvelimexcased  35259  regsfromsetind  36767  wl-equsb3  37927  wl-sbcom2d-lem1  37930  wl-euequf  37945