Theorem cnelprrecn 8043

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 8031	. 2 ⊢ ℂ ∈ V
2	1	prid2 3739	1 ⊢ ℂ ∈ {ℝ, ℂ}

Syntax hints:   ∈ wcel 2175  {cpr 3633  ℂcc 7905  ℝcr 7906

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 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186  ax-cnex 7998

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-v 2773  df-un 3169  df-sn 3638  df-pr 3639

This theorem is referenced by:  dvfcnpm  15080  dvexp  15101  dvmptcmulcn  15111  dvmptnegcn  15112  dvmptsubcn  15113  dvply1  15155