Theorem wl-nfnae1 38278

Description: Unlike nfnae 2465, this specialized theorem avoids ax-11 2194. (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 38277	. 2 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥
2	1	nfn 1890	1 ⊢ Ⅎ𝑥 ¬ ∀𝑦 𝑦 = 𝑥

This proof depends on syntax axioms:  ¬ wn 3  ∀wal 1568  Ⅎwnf 1816

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-10 2178  ax-12 2215  ax-13 2403

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-ex 1813  df-nf 1817

This theorem is used by:  wl-cbvalnaed  38282  wl-2sb6d  38308