Theorem nfna1 2149

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2154 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 2148	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1860	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1539  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 2137

This theorem depends on definitions:  df-bi 206  df-or 846  df-ex 1782  df-nf 1786

This theorem is referenced by:  dvelimhw  2341  nfeqf  2379  equs5  2458  sb4b  2473  nfsb2  2481  ab0OLD  4340  wl-equsb3  36084  wl-sbcom2d-lem1  36087  wl-euequf  36102  wl-ax11-lem3  36112  wl-ax11-lem4  36113  wl-ax11-lem6  36115  wl-ax11-lem7  36116