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Theorem rspesbca 3241
 Description: Existence form of rspsbca 3240. (Contributed by NM, 29-Feb-2008.) (Proof shortened by Mario Carneiro, 13-Oct-2016.)
Assertion
Ref Expression
rspesbca
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rspesbca
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 3164 . . 3
21rspcev 3052 . 2
3 cbvrexsv 2944 . 2
42, 3sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wsb 1658   wcel 1725  wrex 2706  wsbc 3161 This theorem is referenced by:  spesbc  3242  indexfi  7414  indexdom  26436 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-rex 2711  df-v 2958  df-sbc 3162
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