Theorem nfna1 2029

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2034 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 2028	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1784	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1481  Ⅎwnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-10 2019

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710

This theorem is referenced by:  dvelimhw  2173  nfeqf  2301  equs5  2351  nfsb2  2360  wl-equsb3  33337  wl-sbcom2d-lem1  33342  wl-ax11-lem3  33364  wl-ax11-lem4  33365  wl-ax11-lem6  33367  wl-ax11-lem7  33368