Theorem cnelprrecn 8279

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

Assertion

Ref	Expression
cnelprrecn	|- CC e. { RR , CC }

Proof of Theorem cnelprrecn

Step	Hyp	Ref	Expression
1		cnex 8267	. 2 |- CC e. _V
2	1	prid2 3803	1 |- CC e. { RR , CC }

Syntax hints:   e. wcel 2205   {cpr 3695   CCcc 8141   RRcr 8142

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216  ax-cnex 8234

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-v 2817  df-un 3218  df-sn 3700  df-pr 3701

This theorem is referenced by:  dvfcnpm  15681  dvexp  15702  dvmptcmulcn  15712  dvmptnegcn  15713  dvmptsubcn  15714  dvply1  15756