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Theorem cnelprrecn 7457
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 7445 . 2 ℂ ∈ V
21prid2 3544 1 ℂ ∈ {ℝ, ℂ}
Colors of variables: wff set class
Syntax hints:  wcel 1438  {cpr 3442  cc 7327  cr 7328
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-cnex 7415
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3001  df-sn 3447  df-pr 3448
This theorem is referenced by: (None)
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