Theorem rexlimdvw

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by NM, 18-Jun-2014)

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

Proof

Step	Hyp	Ref	Expression
1		rexlimdvw.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	a1d	⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 → ( 𝜓 → 𝜒 ) ) )
3	2	rexlimdv	⊢ ( 𝜑 → ( ∃ 𝑥 ∈ 𝐴 𝜓 → 𝜒 ) )