Theorem eumo

Description: Existential uniqueness implies uniqueness. (Contributed by NM, 23-Mar-1995)

	Ref	Expression
Assertion	eumo	⊢ ( ∃! 𝑥 𝜑 → ∃* 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		df-eu	⊢ ( ∃! 𝑥 𝜑 ↔ ( ∃ 𝑥 𝜑 ∧ ∃* 𝑥 𝜑 ) )
2	1	simprbi	⊢ ( ∃! 𝑥 𝜑 → ∃* 𝑥 𝜑 )