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Theorem reelprrecn 7778
Description: Reals are a subset of the pair of real and complex numbers (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
reelprrecn  |-  RR  e.  { RR ,  CC }

Proof of Theorem reelprrecn
StepHypRef Expression
1 reex 7777 . 2  |-  RR  e.  _V
21prid1 3636 1  |-  RR  e.  { RR ,  CC }
Colors of variables: wff set class
Syntax hints:    e. wcel 1481   {cpr 3532   CCcc 7641   RRcr 7642
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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4053  ax-cnex 7734  ax-resscn 7735
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3079  df-in 3081  df-ss 3088  df-sn 3537  df-pr 3538
This theorem is referenced by:  dvfpm  12864  dvmptcjx  12892
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