Theorem rexlimiva

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by NM, 18-Dec-2006)

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

Proof

Step	Hyp	Ref	Expression
1		rexlimiva.1	⊢ ( ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) → 𝜓 )
2	1	ex	⊢ ( 𝑥 ∈ 𝐴 → ( 𝜑 → 𝜓 ) )
3	2	rexlimiv	⊢ ( ∃ 𝑥 ∈ 𝐴 𝜑 → 𝜓 )