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Mirrors > Home > ILE Home > Th. List > cnelprrecn | GIF version |
Description: Complex numbers are a subset of the pair of real and complex numbers (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
cnelprrecn | ⊢ ℂ ∈ {ℝ, ℂ} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnex 7966 | . 2 ⊢ ℂ ∈ V | |
2 | 1 | prid2 3714 | 1 ⊢ ℂ ∈ {ℝ, ℂ} |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 {cpr 3608 ℂcc 7840 ℝcr 7841 |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-cnex 7933 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-un 3148 df-sn 3613 df-pr 3614 |
This theorem is referenced by: dvfcnpm 14636 dvexp 14652 dvmptcmulcn 14660 dvmptnegcn 14661 dvmptsubcn 14662 |
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