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Theorem ralimdv 2693
 Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 8-Oct-2003.)
Hypothesis
Ref Expression
ralimdv.1 (φ → (ψχ))
Assertion
Ref Expression
ralimdv (φ → (x A ψx A χ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)   A(x)

Proof of Theorem ralimdv
StepHypRef Expression
1 ralimdv.1 . . 3 (φ → (ψχ))
21adantr 451 . 2 ((φ x A) → (ψχ))
32ralimdva 2692 1 (φ → (x A ψx A χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1710  ∀wral 2614 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-ral 2619 This theorem is referenced by:  dffo4  5423  dffo5  5424  isoini2  5498
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