Theorem cnelprrecn 7399

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 7387	. 2 ⊢ ℂ ∈ V
2	1	prid2 3526	1 ⊢ ℂ ∈ {ℝ, ℂ}

Syntax hints:   ∈ wcel 1436  {cpr 3426  ℂcc 7269  ℝcr 7270

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067  ax-cnex 7357

This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2616  df-un 2990  df-sn 3431  df-pr 3432

This theorem is referenced by: (None)