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Theorem rspsbc 2897
 Description: Restricted quantifier version of Axiom 4 of [Mendelson] p. 69. This provides an axiom for a predicate calculus for a restricted domain. This theorem generalizes the unrestricted stdpc4 1699 and spsbc 2827. See also rspsbca 2898 and rspcsbela . (Contributed by NM, 17-Nov-2006.) (Proof shortened by Mario Carneiro, 13-Oct-2016.)
Assertion
Ref Expression
rspsbc
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rspsbc
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvralsv 2589 . 2
2 dfsbcq2 2819 . . 3
32rspcv 2698 . 2
41, 3syl5bi 150 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1434  wsb 1686  wral 2349  wsbc 2816 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-v 2604  df-sbc 2817 This theorem is referenced by:  rspsbca  2898  sbcth2  2902  rspcsbela  2962  riota5f  5523  riotass2  5525  fzrevral  9198
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