Theorem nfna1 2152

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2157 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 2151	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1853	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1531  Ⅎwnf 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-10 2141

This theorem depends on definitions:  df-bi 209  df-or 844  df-ex 1777  df-nf 1781

This theorem is referenced by:  dvelimhw  2362  nfeqf  2395  equs5  2479  sb4b  2495  nfsb2  2518  nfsb2ALT  2596  wl-equsb3  34786  wl-sbcom2d-lem1  34789  wl-euequf  34804  wl-ax11-lem3  34813  wl-ax11-lem4  34814  wl-ax11-lem6  34816  wl-ax11-lem7  34817