Theorem nfna1 2146

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2150 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 2145	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1902	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1599  Ⅎwnf 1827

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-10 2135

This theorem depends on definitions:  df-bi 199  df-or 837  df-ex 1824  df-nf 1828

This theorem is referenced by:  dvelimhw  2314  nfeqf  2345  equs5  2426  nfsb2  2436  wl-equsb3  33932  wl-sbcom2d-lem1  33936  wl-euequf  33950  wl-ax11-lem3  33958  wl-ax11-lem4  33959  wl-ax11-lem6  33961  wl-ax11-lem7  33962