Theorem nfna1 2142

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2147 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 2141	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1853	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1532  Ⅎwnf 1778

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-10 2130

This theorem depends on definitions:  df-bi 206  df-or 846  df-ex 1775  df-nf 1779

This theorem is referenced by:  dvelimhw  2336  nfeqf  2375  equs5  2454  sb4b  2469  nfsb2  2477  ab0OLD  4380  wl-equsb3  37251  wl-sbcom2d-lem1  37254  wl-euequf  37269  wl-ax11-lem3  37282  wl-ax11-lem4  37283  wl-ax11-lem6  37285  wl-ax11-lem7  37286