Theorem nfeu1

Description: Bound-variable hypothesis builder for uniqueness. See also nfeu1ALT . (Contributed by NM, 9-Jul-1994) (Revised by Mario Carneiro, 7-Oct-2016)

	Ref	Expression
Assertion	nfeu1	⊢ Ⅎ 𝑥 ∃! 𝑥 𝜑

Proof

Step	Hyp	Ref	Expression
1		eu6	⊢ ( ∃! 𝑥 𝜑 ↔ ∃ 𝑦 ∀ 𝑥 ( 𝜑 ↔ 𝑥 = 𝑦 ) )
2		nfa1	⊢ Ⅎ 𝑥 ∀ 𝑥 ( 𝜑 ↔ 𝑥 = 𝑦 )
3	2	nfex	⊢ Ⅎ 𝑥 ∃ 𝑦 ∀ 𝑥 ( 𝜑 ↔ 𝑥 = 𝑦 )
4	1 3	nfxfr	⊢ Ⅎ 𝑥 ∃! 𝑥 𝜑