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 1865	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1541  Ⅎwnf 1791

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-10 2143

This theorem depends on definitions:  df-bi 210  df-or 848  df-ex 1788  df-nf 1792

This theorem is referenced by:  dvelimhw  2347  nfeqf  2380  equs5  2459  sb4b  2474  nfsb2  2486  ab0OLD  4276  wl-equsb3  35397  wl-sbcom2d-lem1  35400  wl-euequf  35415  wl-ax11-lem3  35424  wl-ax11-lem4  35425  wl-ax11-lem6  35427  wl-ax11-lem7  35428