Theorem reelprrecn 7627

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

Assertion

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

Proof of Theorem reelprrecn

Step	Hyp	Ref	Expression
1		reex 7626	. 2 |- RR e. _V
2	1	prid1 3576	1 |- RR e. { RR , CC }

Syntax hints:   e. wcel 1448   {cpr 3475   CCcc 7498   RRcr 7499

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082  ax-sep 3986  ax-cnex 7586  ax-resscn 7587

This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-v 2643  df-un 3025  df-in 3027  df-ss 3034  df-sn 3480  df-pr 3481

This theorem is referenced by:  dvfpm  12531