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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 8765 | . 2 ⊢ 4 ∈ ℝ | |
2 | 1 | recni 7746 | 1 ⊢ 4 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 ℂcc 7586 4c4 8741 |
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-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-resscn 7680 ax-1re 7682 ax-addrcl 7685 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-in 3047 df-ss 3054 df-2 8747 df-3 8748 df-4 8749 |
This theorem is referenced by: 5m1e4 8810 4p2e6 8831 4p3e7 8832 4p4e8 8833 4t2e8 8846 4d2e2 8848 8th4div3 8907 div4p1lem1div2 8941 5p5e10 9220 4t4e16 9248 6t5e30 9256 fzo0to42pr 9965 fldiv4p1lem1div2 10046 sq4e2t8 10358 sqoddm1div8 10412 4bc3eq4 10487 4bc2eq6 10488 resqrexlemover 10750 resqrexlemcalc1 10754 resqrexlemcalc3 10756 cos2bnd 11394 flodddiv4 11558 6gcd4e2 11610 6lcm4e12 11695 dveflem 12782 sincosq4sgn 12837 cosq23lt0 12841 sincos6thpi 12850 ex-exp 12866 ex-fac 12867 ex-bc 12868 |
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