Theorem rexex

Description: Restricted existence implies existence. (Contributed by NM, 11-Nov-1995)

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

Proof

Step	Hyp	Ref	Expression
1		df-rex	⊢ ( ∃ 𝑥 ∈ 𝐴 𝜑 ↔ ∃ 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) )
2		exsimpr	⊢ ( ∃ 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) → ∃ 𝑥 𝜑 )
3	1 2	sylbi	⊢ ( ∃ 𝑥 ∈ 𝐴 𝜑 → ∃ 𝑥 𝜑 )