Metamath Proof Explorer


Theorem reurex

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

Ref Expression
Assertion reurex ( ∃! 𝑥𝐴 𝜑 → ∃ 𝑥𝐴 𝜑 )

Proof

Step Hyp Ref Expression
1 reu5 ( ∃! 𝑥𝐴 𝜑 ↔ ( ∃ 𝑥𝐴 𝜑 ∧ ∃* 𝑥𝐴 𝜑 ) )
2 1 simplbi ( ∃! 𝑥𝐴 𝜑 → ∃ 𝑥𝐴 𝜑 )