Metamath Proof Explorer


Theorem reximdvai

Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of Margaris p. 90. (Contributed by NM, 14-Nov-2002) Reduce dependencies on axioms. (Revised by Wolf Lammen, 8-Jan-2020)

Ref Expression
Hypothesis reximdvai.1 φ x A ψ χ
Assertion reximdvai φ x A ψ x A χ

Proof

Step Hyp Ref Expression
1 reximdvai.1 φ x A ψ χ
2 1 ralrimiv φ x A ψ χ
3 rexim x A ψ χ x A ψ x A χ
4 2 3 syl φ x A ψ x A χ