Theorem reurex

Description: Restricted unique existence implies restricted existence. (Contributed by NM, 19-Aug-1999)

	Ref	Expression
Assertion	reurex	⊢ ( ∃! 𝑥 ∈ 𝐴 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		reu5	⊢ ( ∃! 𝑥 ∈ 𝐴 𝜑 ↔ ( ∃ 𝑥 ∈ 𝐴 𝜑 ∧ ∃* 𝑥 ∈ 𝐴 𝜑 ) )
2	1	simplbi	⊢ ( ∃! 𝑥 ∈ 𝐴 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜑 )