Theorem nfna1 2150

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2155 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 2149	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1855	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1535  Ⅎwnf 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-10 2139

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1777  df-nf 1781

This theorem is referenced by:  dvelimhw  2346  nfeqf  2384  equs5  2463  sb4b  2478  nfsb2  2486  dvelimalcased  35068  dvelimexcased  35070  wl-equsb3  37537  wl-sbcom2d-lem1  37540  wl-euequf  37555  wl-ax11-lem3  37568  wl-ax11-lem4  37569  wl-ax11-lem6  37571  wl-ax11-lem7  37572