Theorem nfna1 2026

Description: A convenience theorem particularly designed to remove dependencies on ax-11 2031 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 2025	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfn 1781	1 ⊢ Ⅎ𝑥 ¬ ∀𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1478  Ⅎwnf 1705

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-10 2016

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1702  df-nf 1707

This theorem is referenced by:  dvelimhw  2170  nfeqf  2300  equs5  2350  nfsb2  2359  wl-equsb3  33008  wl-sbcom2d-lem1  33013  wl-ax11-lem3  33035  wl-ax11-lem4  33036  wl-ax11-lem6  33038  wl-ax11-lem7  33039