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Theorem cnelprrecn 7720
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 7708 . 2  |-  CC  e.  _V
21prid2 3598 1  |-  CC  e.  { RR ,  CC }
Colors of variables: wff set class
Syntax hints:    e. wcel 1463   {cpr 3496   CCcc 7582   RRcr 7583
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-cnex 7675
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-sn 3501  df-pr 3502
This theorem is referenced by:  dvfcnpm  12734  dvexp  12750  dvmptcmulcn  12758  dvmptnegcn  12759  dvmptsubcn  12760
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