Theorem reximi

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 18-Oct-1996)

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

Proof

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