Theorem wl-nfnae1 38127

Description: Unlike nfnae 2464, this specialized theorem avoids ax-11 2190. (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 38126	. 2 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥
2	1	nfn 1885	1 ⊢ Ⅎ𝑥 ¬ ∀𝑦 𝑦 = 𝑥

Syntax hints:  ¬ wn 3  ∀wal 1566  Ⅎwnf 1811

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-10 2174  ax-12 2211  ax-13 2402

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-ex 1808  df-nf 1812

This theorem is referenced by:  wl-cbvalnaed  38131  wl-2sb6d  38157