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Theorem ralimdva 2381
Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 22-May-1999.)
Hypothesis
Ref Expression
ralimdva.1 ((φ x A) → (ψχ))
Assertion
Ref Expression
ralimdva (φ → (x A ψx A χ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)   A(x)

Proof of Theorem ralimdva
StepHypRef Expression
1 nfv 1418 . 2 xφ
2 ralimdva.1 . 2 ((φ x A) → (ψχ))
31, 2ralimdaa 2380 1 (φ → (x A ψx A χ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wcel 1390  wral 2300
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305
This theorem is referenced by:  ralimdv  2382  f1mpt  5353  isores3  5398  caofrss  5677  caoftrn  5678  tfrlemibxssdm  5882  rdgon  5913  indstr  8312
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