Theorem cnelprrecn 8135

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 8123	. 2 |- CC e. _V
2	1	prid2 3773	1 |- CC e. { RR , CC }

Syntax hints:   e. wcel 2200   {cpr 3667   CCcc 7997   RRcr 7998

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211  ax-cnex 8090

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-un 3201  df-sn 3672  df-pr 3673

This theorem is referenced by:  dvfcnpm  15364  dvexp  15385  dvmptcmulcn  15395  dvmptnegcn  15396  dvmptsubcn  15397  dvply1  15439