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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 7712 | . 2 ⊢ ℂ ∈ V | |
2 | 1 | prid2 3600 | 1 ⊢ ℂ ∈ {ℝ, ℂ} |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 {cpr 3498 ℂcc 7586 ℝcr 7587 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-cnex 7679 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 |
This theorem is referenced by: dvfcnpm 12755 dvexp 12771 dvmptcmulcn 12779 dvmptnegcn 12780 dvmptsubcn 12781 |
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