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Theorem ralrimivw 2698
 Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 18-Jun-2014.)
Hypothesis
Ref Expression
ralrimivw.1 (φψ)
Assertion
Ref Expression
ralrimivw (φx A ψ)
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem ralrimivw
StepHypRef Expression
1 ralrimivw.1 . . 3 (φψ)
21a1d 22 . 2 (φ → (x Aψ))
32ralrimiv 2696 1 (φx A ψ)
 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-ex 1542  df-nf 1545  df-ral 2619 This theorem is referenced by:  2rmorex  3040  riinrab  4041  nnadjoinpw  4521  dmxp  4923  eqfnfv  5392  mpteq12dv  5656  mpt2eq12  5662  clos1nrel  5886  uniqs  5984  enprmaplem5  6080  nchoicelem6  6294  dmfrec  6316
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