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 1537  Ⅎwnf 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-10 2137

This theorem depends on definitions:  df-bi 206  df-or 845  df-ex 1783  df-nf 1787

This theorem is referenced by:  dvelimhw  2343  nfeqf  2381  equs5  2460  sb4b  2475  nfsb2  2487  ab0OLD  4309  wl-equsb3  35711  wl-sbcom2d-lem1  35714  wl-euequf  35729  wl-ax11-lem3  35738  wl-ax11-lem4  35739  wl-ax11-lem6  35741  wl-ax11-lem7  35742