Theorem nfna1 2151

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2156 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 2150	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1861	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1537  Ⅎwnf 1787

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-10 2139

This theorem depends on definitions:  df-bi 206  df-or 844  df-ex 1784  df-nf 1788

This theorem is referenced by:  dvelimhw  2345  nfeqf  2381  equs5  2460  sb4b  2475  nfsb2  2487  ab0OLD  4306  wl-equsb3  35638  wl-sbcom2d-lem1  35641  wl-euequf  35656  wl-ax11-lem3  35665  wl-ax11-lem4  35666  wl-ax11-lem6  35668  wl-ax11-lem7  35669