Theorem rexlimivw

Description: Weaker version of rexlimiv . (Contributed by FL, 19-Sep-2011)

	Ref	Expression
Hypothesis	rexlimivw.1	⊢ ( 𝜑 → 𝜓 )
Assertion	rexlimivw	⊢ ( ∃ 𝑥 ∈ 𝐴 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		rexlimivw.1	⊢ ( 𝜑 → 𝜓 )
2	1	a1i	⊢ ( 𝑥 ∈ 𝐴 → ( 𝜑 → 𝜓 ) )
3	2	rexlimiv	⊢ ( ∃ 𝑥 ∈ 𝐴 𝜑 → 𝜓 )