Theorem wl-nfnae1 38211

Description: Unlike nfnae 2465, this specialized theorem avoids ax-11 2191. (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 38210	. 2 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥
2	1	nfn 1886	1 ⊢ Ⅎ𝑥 ¬ ∀𝑦 𝑦 = 𝑥

This proof depends on syntax axioms:  ¬ wn 3  ∀wal 1567  Ⅎwnf 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-10 2175  ax-12 2212  ax-13 2403

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-ex 1809  df-nf 1813

This theorem is used by:  wl-cbvalnaed  38215  wl-2sb6d  38241