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Theorem cnelprrecn 7724
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 ℂ ∈ {ℝ, ℂ}

Proof of Theorem cnelprrecn
StepHypRef Expression
1 cnex 7712 . 2 ℂ ∈ V
21prid2 3600 1 ℂ ∈ {ℝ, ℂ}
Colors of variables: wff set class
Syntax hints:  wcel 1465  {cpr 3498  cc 7586  cr 7587
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-cnex 7679
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045  df-sn 3503  df-pr 3504
This theorem is referenced by:  dvfcnpm  12755  dvexp  12771  dvmptcmulcn  12779  dvmptnegcn  12780  dvmptsubcn  12781
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