Theorem nfeuw

Description: Bound-variable hypothesis builder for the unique existential quantifier. Version of nfeu with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 8-Mar-1995) Avoid ax-13 . (Revised by Gino Giotto, 10-Jan-2024)

	Ref	Expression
Hypothesis	nfeuw.1	⊢ Ⅎ 𝑥 𝜑
Assertion	nfeuw	⊢ Ⅎ 𝑥 ∃! 𝑦 𝜑

Proof

Step	Hyp	Ref	Expression
1		nfeuw.1	⊢ Ⅎ 𝑥 𝜑
2		nftru	⊢ Ⅎ 𝑦 ⊤
3	1	a1i	⊢ ( ⊤ → Ⅎ 𝑥 𝜑 )
4	2 3	nfeudw	⊢ ( ⊤ → Ⅎ 𝑥 ∃! 𝑦 𝜑 )
5	4	mptru	⊢ Ⅎ 𝑥 ∃! 𝑦 𝜑