Theorem rexlimivw

Description: Weaker version of rexlimiv . (Contributed by FL, 19-Sep-2011) (Proof shortened by Wolf Lammen, 23-Dec-2024)

	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	adantl	⊢ ( ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) → 𝜓 )
3	2	rexlimiva	⊢ ( ∃ 𝑥 ∈ 𝐴 𝜑 → 𝜓 )