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Theorem reelprrecn 7959
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 7958 . 2  |-  RR  e.  _V
21prid1 3710 1  |-  RR  e.  { RR ,  CC }
Colors of variables: wff set class
Syntax hints:    e. wcel 2158   {cpr 3605   CCcc 7822   RRcr 7823
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169  ax-sep 4133  ax-cnex 7915  ax-resscn 7916
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-un 3145  df-in 3147  df-ss 3154  df-sn 3610  df-pr 3611
This theorem is referenced by:  dvfpm  14429  dvmptcjx  14457
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