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Mirrors > Home > ILE Home > Th. List > 4cn | GIF version |
Description: The number 4 is a complex number. (Contributed by David A. Wheeler, 7-Jul-2016.) |
Ref | Expression |
---|---|
4cn | ⊢ 4 ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 4re 8655 | . 2 ⊢ 4 ∈ ℝ | |
2 | 1 | recni 7650 | 1 ⊢ 4 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1448 ℂcc 7498 4c4 8631 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-11 1452 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-resscn 7587 ax-1re 7589 ax-addrcl 7592 |
This theorem depends on definitions: df-bi 116 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-in 3027 df-ss 3034 df-2 8637 df-3 8638 df-4 8639 |
This theorem is referenced by: 4p2e6 8715 4p3e7 8716 4p4e8 8717 4t2e8 8730 4d2e2 8732 8th4div3 8791 div4p1lem1div2 8825 5p5e10 9104 4t4e16 9132 6t5e30 9140 fzo0to42pr 9838 fldiv4p1lem1div2 9919 sq4e2t8 10231 sqoddm1div8 10285 4bc3eq4 10360 4bc2eq6 10361 resqrexlemover 10622 resqrexlemcalc1 10626 resqrexlemcalc3 10628 cos2bnd 11265 flodddiv4 11426 6gcd4e2 11476 6lcm4e12 11561 ex-exp 12542 ex-fac 12543 ex-bc 12544 |
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