Metamath Proof Explorer


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