Theorem reximdv

Description: Deduction from Theorem 19.22 of Margaris p. 90. (Restricted quantifier version with strong hypothesis.) (Contributed by NM, 24-Jun-1998)

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

Proof

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