Theorem wl-naevhba1v

Description: An instance of hbn1w applied to equality. (Contributed by Wolf Lammen, 7-Apr-2021)

	Ref	Expression
Assertion	wl-naevhba1v	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑥 ¬ ∀ 𝑥 𝑥 = 𝑦 )

Proof

Step	Hyp	Ref	Expression
1		equequ1	⊢ ( 𝑥 = 𝑧 → ( 𝑥 = 𝑦 ↔ 𝑧 = 𝑦 ) )
2	1	hbn1w	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑥 ¬ ∀ 𝑥 𝑥 = 𝑦 )