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 1856	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1535  Ⅎwnf 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-10 2141

This theorem depends on definitions:  df-bi 207  df-or 847  df-ex 1778  df-nf 1782

This theorem is referenced by:  dvelimhw  2351  nfeqf  2389  equs5  2468  sb4b  2483  nfsb2  2491  ab0OLD  4403  dvelimalcased  35051  dvelimexcased  35053  wl-equsb3  37510  wl-sbcom2d-lem1  37513  wl-euequf  37528  wl-ax11-lem3  37541  wl-ax11-lem4  37542  wl-ax11-lem6  37544  wl-ax11-lem7  37545