Theorem nfna1 2176

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2181 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 2175	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1931	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1628  Ⅎwnf 1855

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-10 2166

This theorem depends on definitions:  df-bi 197  df-or 384  df-ex 1852  df-nf 1857

This theorem is referenced by:  dvelimhw  2316  nfeqf  2444  equs5  2486  nfsb2  2495  wl-equsb3  33648  wl-sbcom2d-lem1  33653  wl-ax11-lem3  33675  wl-ax11-lem4  33676  wl-ax11-lem6  33678  wl-ax11-lem7  33679