Theorem nfna1 2186

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2191 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 2185	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1886	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

This proof depends on syntax axioms:  ¬ wn 3  ∀wal 1567  Ⅎwnf 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-10 2175

This proof depends on definitions:  df-bi 210  df-or 861  df-ex 1809  df-nf 1813

This theorem is used by:  dvelimhw  2376  nfeqf  2412  equs5  2491  sb4b  2506  nfsb2  2514  dvelimalcased  35472  dvelimexcased  35474  regsfromsetind  37078  wl-equsb3  38239  wl-sbcom2d-lem1  38242  wl-euequf  38257