Theorem euabex

Description: The abstraction of a wff with existential uniqueness exists. (Contributed by NM, 25-Nov-1994)

	Ref	Expression
Assertion	euabex	⊢ ( ∃! 𝑥 𝜑 → { 𝑥 ∣ 𝜑 } ∈ V )

Proof

Step	Hyp	Ref	Expression
1		eumo	⊢ ( ∃! 𝑥 𝜑 → ∃* 𝑥 𝜑 )
2		moabex	⊢ ( ∃* 𝑥 𝜑 → { 𝑥 ∣ 𝜑 } ∈ V )
3	1 2	syl	⊢ ( ∃! 𝑥 𝜑 → { 𝑥 ∣ 𝜑 } ∈ V )