Theorem nfna1 2089

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2093 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 2088	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1819	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1505  Ⅎwnf 1746

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-10 2079

This theorem depends on definitions:  df-bi 199  df-or 834  df-ex 1743  df-nf 1747

This theorem is referenced by:  dvelimhw  2279  nfeqf  2311  equs5  2397  nfsb2  2443  nfsb2ALT  2527  wl-equsb3  34233  wl-sbcom2d-lem1  34236  wl-euequf  34251  wl-ax11-lem3  34260  wl-ax11-lem4  34261  wl-ax11-lem6  34263  wl-ax11-lem7  34264