Theorem nfna1 2155

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2160 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 2154	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1858	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1539  Ⅎwnf 1784

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-10 2144

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1781  df-nf 1785

This theorem is referenced by:  dvelimhw  2345  nfeqf  2381  equs5  2460  sb4b  2475  nfsb2  2483  dvelimalcased  35087  dvelimexcased  35089  wl-equsb3  37600  wl-sbcom2d-lem1  37603  wl-euequf  37618