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Mirrors > Home > ILE Home > Th. List > 3cn | GIF version |
Description: The number 3 is a complex number. (Contributed by FL, 17-Oct-2010.) |
Ref | Expression |
---|---|
3cn | ⊢ 3 ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3re 8991 | . 2 ⊢ 3 ∈ ℝ | |
2 | 1 | recni 7968 | 1 ⊢ 3 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2148 ℂcc 7808 3c3 8969 |
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-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-resscn 7902 ax-1re 7904 ax-addrcl 7907 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-in 3135 df-ss 3142 df-2 8976 df-3 8977 |
This theorem is referenced by: 3ex 8993 3m1e2 9037 4m1e3 9038 3p2e5 9058 3p3e6 9059 4p4e8 9062 5p4e9 9065 3t1e3 9072 3t2e6 9073 3t3e9 9074 8th4div3 9136 halfpm6th 9137 6p4e10 9453 9t8e72 9509 halfthird 9524 fzo0to42pr 10217 sq3 10613 expnass 10622 fac3 10707 4bc3eq4 10748 ef01bndlem 11759 sin01bnd 11760 cos01bnd 11761 cos1bnd 11762 cos2bnd 11763 cos01gt0 11765 3dvdsdec 11864 3dvds2dec 11865 3lcm2e6woprm 12080 cosq23lt0 14147 tangtx 14152 sincos6thpi 14156 sincos3rdpi 14157 pigt3 14158 binom4 14290 lgsdir2lem1 14322 lgsdir2lem5 14326 ex-exp 14361 ex-dvds 14364 ex-gcd 14365 |
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