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Mirrors > Home > ILE Home > Th. List > cnelprrecn | Unicode 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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnex 7856 | . 2 | |
2 | 1 | prid2 3666 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2128 cpr 3561 cc 7730 cr 7731 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 ax-cnex 7823 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-sn 3566 df-pr 3567 |
This theorem is referenced by: dvfcnpm 13059 dvexp 13075 dvmptcmulcn 13083 dvmptnegcn 13084 dvmptsubcn 13085 |
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