Theorem nfna1 2153

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2158 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 2152	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1857	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1538  Ⅎwnf 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-10 2142

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1780  df-nf 1784

This theorem is referenced by:  dvelimhw  2343  nfeqf  2380  equs5  2459  sb4b  2474  nfsb2  2482  dvelimalcased  35073  dvelimexcased  35075  wl-equsb3  37541  wl-sbcom2d-lem1  37544  wl-euequf  37559  wl-ax11-lem3  37572  wl-ax11-lem4  37573  wl-ax11-lem6  37575  wl-ax11-lem7  37576