Theorem nfna1 2188

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2193 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 2187	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1889	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

This proof depends on syntax axioms:  ¬ wn 3  ∀wal 1567  Ⅎwnf 1815

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-10 2177

This proof depends on definitions:  df-bi 210  df-or 862  df-ex 1812  df-nf 1816

This theorem is used by:  dvelimhw  2374  nfeqf  2410  equs5  2489  sb4b  2504  nfsb2  2512  dvelimalcased  35705  dvelimexcased  35707  regsfromsetind  37327  wl-equsb3  38489  wl-sbcom2d-lem1  38492  wl-euequf  38507