Theorem wl-nfnae1 37912

Description: Unlike nfnae 2444, this specialized theorem avoids ax-11 2170. (Contributed by Wolf Lammen, 27-Jun-2019.)

Assertion

Ref	Expression
wl-nfnae1	⊢ Ⅎ𝑥 ¬ ∀𝑦 𝑦 = 𝑥

Proof of Theorem wl-nfnae1

Step	Hyp	Ref	Expression
1		wl-nfae1 37911	. 2 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥
2	1	nfn 1865	1 ⊢ Ⅎ𝑥 ¬ ∀𝑦 𝑦 = 𝑥

Syntax hints:  ¬ wn 3  ∀wal 1546  Ⅎwnf 1791

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1975  ax-7 2016  ax-10 2154  ax-12 2191  ax-13 2382

This theorem depends on definitions:  df-bi 209  df-an 398  df-or 855  df-ex 1788  df-nf 1792

This theorem is referenced by:  wl-cbvalnaed  37916  wl-2sb6d  37942