Theorem nfna1 2158

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2163 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 2157	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1859	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1540  Ⅎwnf 1785

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-10 2147

This theorem depends on definitions:  df-bi 207  df-or 849  df-ex 1782  df-nf 1786

This theorem is referenced by:  dvelimhw  2348  nfeqf  2384  equs5  2463  sb4b  2478  nfsb2  2486  dvelimalcased  35210  dvelimexcased  35212  wl-equsb3  37730  wl-sbcom2d-lem1  37733  wl-euequf  37748