Theorem cnelprrecn 11245

Description: Complex numbers are a subset of the pair of real and complex numbers . (Contributed by David A. Wheeler, 8-Dec-2018.)

Assertion

Ref	Expression
cnelprrecn	⊢ ℂ ∈ {ℝ, ℂ}

Proof of Theorem cnelprrecn

Step	Hyp	Ref	Expression
1		cnex 11233	. 2 ⊢ ℂ ∈ V
2	1	prid2 4767	1 ⊢ ℂ ∈ {ℝ, ℂ}

Syntax hints:   ∈ wcel 2105  {cpr 4632  ℂcc 11150  ℝcr 11151

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705  ax-cnex 11208

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1539  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-v 3479  df-un 3967  df-sn 4631  df-pr 4633

This theorem is referenced by:  dvfcn  25957  dvnres  25981  dvexp  26005  dvrecg  26025  dvexp3  26030  dvef  26032  dvsincos  26033  dvlipcn  26047  dv11cn  26054  dvply1  26339  dvtaylp  26426  pserdvlem2  26486  pige3ALT  26576  dvlog  26707  advlogexp  26711  logtayl  26716  dvcxp1  26796  dvcxp2  26797  dvcncxp1  26799  dvatan  26992  efrlim  27026  efrlimOLD  27027  lgamgulmlem2  27087  logdivsum  27591  log2sumbnd  27602  itgexpif  34599  dvtan  37656  dvasin  37690  dvacos  37691  lcmineqlem7  42016  lcmineqlem8  42017  lcmineqlem12  42021  dvrelogpow2b  42049  aks4d1p1p6  42054  readvrec2  42369  readvrec  42370  lhe4.4ex1a  44324  expgrowthi  44328  expgrowth  44330  binomcxplemdvbinom  44348  binomcxplemnotnn0  44351  dvsinexp  45866  dvsinax  45868  dvasinbx  45875  dvcosax  45881  dvxpaek  45895  itgsincmulx  45929  fourierdlem56  46117  etransclem46  46235