Theorem nfna1 2189

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2194 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 2188	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1890	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

This proof depends on syntax axioms:  ¬ wn 3  ∀wal 1568  Ⅎwnf 1816

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-10 2178

This proof depends on definitions:  df-bi 210  df-or 862  df-ex 1813  df-nf 1817

This theorem is used by:  dvelimhw  2374  nfeqf  2410  equs5  2489  sb4b  2504  nfsb2  2512  dvelimalcased  35639  dvelimexcased  35641  regsfromsetind  37249  wl-equsb3  38408  wl-sbcom2d-lem1  38411  wl-euequf  38426