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Theorem ralrimiv 2696
 Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Nov-1994.)
Hypothesis
Ref Expression
ralrimiv.1 (φ → (x Aψ))
Assertion
Ref Expression
ralrimiv (φx A ψ)
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem ralrimiv
StepHypRef Expression
1 nfv 1619 . 2 xφ
2 ralrimiv.1 . 2 (φ → (x Aψ))
31, 2ralrimi 2695 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:  ralrimiva  2697  ralrimivw  2698  ralrimivv  2705  r19.27av  2752  rr19.3v  2980  rabssdv  3346  rzal  3651  pw1disj  4167  nnadjoin  4520  fmpt2d  5695  nnc3n3p1  6278
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