Metamath Proof Explorer

Theorem ralimdv

Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.20 of Margaris p. 90 ( alim ). (Contributed by NM, 8-Oct-2003)

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


Step Hyp Ref Expression
1 ralimdv.1 φ ψ χ
2 1 adantr φ x A ψ χ
3 2 ralimdva φ x A ψ x A χ