Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  cnelprrecn GIF version

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  ℂcc 7327  ℝcr 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)
 Copyright terms: Public domain W3C validator