Theorem wl-nfnae1

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

	Ref	Expression
Assertion	wl-nfnae1	⊢ Ⅎ 𝑥 ¬ ∀ 𝑦 𝑦 = 𝑥

Proof

Step	Hyp	Ref	Expression
1		wl-nfae1	⊢ Ⅎ 𝑥 ∀ 𝑦 𝑦 = 𝑥
2	1	nfn	⊢ Ⅎ 𝑥 ¬ ∀ 𝑦 𝑦 = 𝑥