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Theorem cnelprrecn 7868
Description: Complex numbers are a subset of the pair of real and complex numbers (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
cnelprrecn  |-  CC  e.  { RR ,  CC }

Proof of Theorem cnelprrecn
StepHypRef Expression
1 cnex 7856 . 2  |-  CC  e.  _V
21prid2 3666 1  |-  CC  e.  { RR ,  CC }
Colors of variables: wff set class
Syntax hints:    e. wcel 2128   {cpr 3561   CCcc 7730   RRcr 7731
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139  ax-cnex 7823
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-sn 3566  df-pr 3567
This theorem is referenced by:  dvfcnpm  13059  dvexp  13075  dvmptcmulcn  13083  dvmptnegcn  13084  dvmptsubcn  13085
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