Theorem reelprrecn 11130

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

Assertion

Ref	Expression
reelprrecn	⊢ ℝ ∈ {ℝ, ℂ}

Proof of Theorem reelprrecn

Step	Hyp	Ref	Expression
1		reex 11129	. 2 ⊢ ℝ ∈ V
2	1	prid1 4706	1 ⊢ ℝ ∈ {ℝ, ℂ}

Syntax hints:   ∈ wcel 2114  {cpr 4569  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 2708  ax-sep 5231  ax-cnex 11094  ax-resscn 11095

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-rab 3390  df-v 3431  df-un 3894  df-in 3896  df-ss 3906  df-sn 4568  df-pr 4570

This theorem is referenced by:  dvf  25874  dvmptresicc  25883  dvmptcj  25935  dvmptre  25936  dvmptim  25937  rolle  25957  cmvth  25958  mvth  25959  dvlip  25960  dvlipcn  25961  dvle  25974  dvivthlem1  25975  dvivth  25977  lhop2  25982  dvcnvre  25986  dvfsumle  25988  dvfsumge  25989  dvfsumabs  25990  dvfsumlem2  25994  dvfsum2  26001  ftc2  26011  itgparts  26014  itgsubstlem  26015  itgpowd  26017  aalioulem3  26300  taylthlem2  26339  taylth  26340  efcvx  26414  pige3ALT  26484  dvrelog  26601  advlog  26618  advlogexp  26619  logccv  26627  dvcxp1  26704  loglesqrt  26725  divsqrtsumlem  26943  lgamgulmlem2  26993  logexprlim  27188  logdivsum  27496  log2sumbnd  27507  fdvneggt  34744  fdvnegge  34746  itgexpif  34750  logdivsqrle  34794  ftc2nc  38023  dvreasin  38027  dvreacos  38028  areacirclem1  38029  dvrelog2  42503  dvrelog3  42504  dvrelog2b  42505  dvrelogpow2b  42507  aks4d1p1p6  42512  redvmptabs  42792  readvrec2  42793  readvrec  42794  readvcot  42796  lhe4.4ex1a  44756  dvcosre  46340  dvcnre  46344  itgsin0pilem1  46378  itgsinexplem1  46382  itgcoscmulx  46397  itgiccshift  46408  itgperiod  46409  itgsbtaddcnst  46410  dirkeritg  46530  dirkercncflem2  46532  fourierdlem28  46563  fourierdlem39  46574  fourierdlem56  46590  fourierdlem57  46591  fourierdlem58  46592  fourierdlem59  46593  fourierdlem60  46594  fourierdlem61  46595  fourierdlem62  46596  fourierdlem68  46602  fourierdlem72  46606  fouriersw  46659  etransclem2  46664  etransclem23  46685  etransclem35  46697  etransclem38  46700  etransclem39  46701  etransclem44  46706  etransclem45  46707  etransclem46  46708  etransclem47  46709