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Theorem reelprrecn 7909
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 7908 . 2 ℝ ∈ V
21prid1 3689 1 ℝ ∈ {ℝ, ℂ}
Colors of variables: wff set class
Syntax hints:  wcel 2141  {cpr 3584  cc 7772  cr 7773
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152  ax-sep 4107  ax-cnex 7865  ax-resscn 7866
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-sn 3589  df-pr 3590
This theorem is referenced by:  dvfpm  13452  dvmptcjx  13480
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