Theorem cnelprrecn 8167

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	⊢ ℂ ∈ {ℝ, ℂ}

Proof of Theorem cnelprrecn

Step	Hyp	Ref	Expression
1		cnex 8155	. 2 ⊢ ℂ ∈ V
2	1	prid2 3778	1 ⊢ ℂ ∈ {ℝ, ℂ}

Syntax hints:   ∈ wcel 2202  {cpr 3670  ℂcc 8029  ℝcr 8030

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213  ax-cnex 8122

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-un 3204  df-sn 3675  df-pr 3676

This theorem is referenced by:  dvfcnpm  15413  dvexp  15434  dvmptcmulcn  15444  dvmptnegcn  15445  dvmptsubcn  15446  dvply1  15488