Theorem nfnaew

Description: All variables are effectively bound in a distinct variable specifier. Version of nfnae with a disjoint variable condition, which does not require ax-13 . (Contributed by Mario Carneiro, 11-Aug-2016) (Revised by Gino Giotto, 10-Jan-2024)

	Ref	Expression
Assertion	nfnaew	⊢ Ⅎ 𝑧 ¬ ∀ 𝑥 𝑥 = 𝑦

Proof

Step	Hyp	Ref	Expression
1		hbaev	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑧 ∀ 𝑥 𝑥 = 𝑦 )
2	1	nf5i	⊢ Ⅎ 𝑧 ∀ 𝑥 𝑥 = 𝑦
3	2	nfn	⊢ Ⅎ 𝑧 ¬ ∀ 𝑥 𝑥 = 𝑦