Theorem cnelprrecn 8211

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 8199	. 2 ⊢ ℂ ∈ V
2	1	prid2 3782	1 ⊢ ℂ ∈ {ℝ, ℂ}

Syntax hints:   ∈ wcel 2202  {cpr 3674  ℂcc 8073  ℝcr 8074

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 2213  ax-cnex 8166

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-v 2805  df-un 3205  df-sn 3679  df-pr 3680

This theorem is referenced by:  dvfcnpm  15484  dvexp  15505  dvmptcmulcn  15515  dvmptnegcn  15516  dvmptsubcn  15517  dvply1  15559