Theorem cnelprrecn 11131

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 11119	. 2 ⊢ ℂ ∈ V
2	1	prid2 4722	1 ⊢ ℂ ∈ {ℝ, ℂ}

Syntax hints:   ∈ wcel 2114  {cpr 4584  ℂcc 11036  ℝcr 11037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-cnex 11094

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3444  df-un 3908  df-sn 4583  df-pr 4585

This theorem is referenced by:  dvfcn  25877  dvnres  25901  dvexp  25925  dvrecg  25945  dvexp3  25950  dvef  25952  dvsincos  25953  dvlipcn  25967  dv11cn  25974  dvply1  26259  dvtaylp  26346  pserdvlem2  26406  pige3ALT  26497  dvlog  26628  advlogexp  26632  logtayl  26637  dvcxp1  26717  dvcxp2  26718  dvcncxp1  26720  dvatan  26913  efrlim  26947  efrlimOLD  26948  lgamgulmlem2  27008  logdivsum  27512  log2sumbnd  27523  itgexpif  34784  dvtan  37921  dvasin  37955  dvacos  37956  lcmineqlem7  42405  lcmineqlem8  42406  lcmineqlem12  42410  dvrelogpow2b  42438  aks4d1p1p6  42443  readvrec2  42731  readvrec  42732  lhe4.4ex1a  44685  expgrowthi  44689  expgrowth  44691  binomcxplemdvbinom  44709  binomcxplemnotnn0  44712  dvsinexp  46269  dvsinax  46271  dvasinbx  46278  dvcosax  46284  dvxpaek  46298  itgsincmulx  46332  fourierdlem56  46520  etransclem46  46638