Theorem nfna1 2156

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2161 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 2155	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1857	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1535  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 2145

This theorem depends on definitions:  df-bi 209  df-or 844  df-ex 1781  df-nf 1785

This theorem is referenced by:  dvelimhw  2366  nfeqf  2399  equs5  2483  sb4b  2499  nfsb2  2522  nfsb2ALT  2600  wl-equsb3  34794  wl-sbcom2d-lem1  34797  wl-euequf  34812  wl-ax11-lem3  34821  wl-ax11-lem4  34822  wl-ax11-lem6  34824  wl-ax11-lem7  34825