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Theorem reelprrecn 7016
 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 ℝ ∈ {ℝ, ℂ}

Proof of Theorem reelprrecn
StepHypRef Expression
1 reex 7015 . 2 ℝ ∈ V
21prid1 3476 1 ℝ ∈ {ℝ, ℂ}
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1393  {cpr 3376  ℂcc 6887  ℝcr 6888 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-cnex 6975  ax-resscn 6976 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-sn 3381  df-pr 3382 This theorem is referenced by: (None)
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