Theorem rexlimdv3a

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). Frequently-used variant of rexlimdv . (Contributed by NM, 7-Jun-2015)

	Ref	Expression
Hypothesis	rexlimdv3a.1	⊢ ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ∧ 𝜓 ) → 𝜒 )
Assertion	rexlimdv3a	⊢ ( 𝜑 → ( ∃ 𝑥 ∈ 𝐴 𝜓 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		rexlimdv3a.1	⊢ ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ∧ 𝜓 ) → 𝜒 )
2	1	3exp	⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 → ( 𝜓 → 𝜒 ) ) )
3	2	rexlimdv	⊢ ( 𝜑 → ( ∃ 𝑥 ∈ 𝐴 𝜓 → 𝜒 ) )