Theorem eumoi

Description: Uniqueness inferred from existential uniqueness. (Contributed by NM, 5-Apr-1995)

	Ref	Expression
Hypothesis	eumoi.1	⊢ ∃! 𝑥 𝜑
Assertion	eumoi	⊢ ∃* 𝑥 𝜑

Proof

Step	Hyp	Ref	Expression
1		eumoi.1	⊢ ∃! 𝑥 𝜑
2		eumo	⊢ ( ∃! 𝑥 𝜑 → ∃* 𝑥 𝜑 )
3	1 2	ax-mp	⊢ ∃* 𝑥 𝜑