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Theorem rspsbc 3239
 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 2091 and spsbc 3173. See also rspsbca 3240 and rspcsbela 3308. (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 2943 . 2
2 dfsbcq2 3164 . . 3
32rspcv 3048 . 2
41, 3syl5bi 209 1
 Colors of variables: wff set class Syntax hints:   wi 4  wsb 1658   wcel 1725  wral 2705  wsbc 3161 This theorem is referenced by:  rspsbca  3240  sbcth2  3244  rspcsbela  3308  riota5f  6574  riotass2  6577  fzrevral  11131  rspsbc2  28618  truniALT  28626  rspsbc2VD  28967  truniALTVD  28990  trintALTVD  28992  trintALT  28993 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-v 2958  df-sbc 3162
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