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Mirrors > Home > MPE Home > Th. List > 6cn | Structured version Visualization version GIF version |
Description: The number 6 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
6cn | ⊢ 6 ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 6re 10978 | . 2 ⊢ 6 ∈ ℝ | |
2 | 1 | recni 9931 | 1 ⊢ 6 ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1977 ℂcc 9813 6c6 10951 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-resscn 9872 ax-1cn 9873 ax-icn 9874 ax-addcl 9875 ax-addrcl 9876 ax-mulcl 9877 ax-mulrcl 9878 ax-i2m1 9883 ax-1ne0 9884 ax-rrecex 9887 ax-cnre 9888 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ne 2782 df-ral 2901 df-rex 2902 df-rab 2905 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-op 4132 df-uni 4373 df-br 4584 df-iota 5768 df-fv 5812 df-ov 6552 df-2 10956 df-3 10957 df-4 10958 df-5 10959 df-6 10960 |
This theorem is referenced by: 7m1e6 11018 6p2e8 11046 6p3e9 11047 6p4e10OLD 11048 halfpm6th 11130 6p4e10 11474 6t2e12 11517 6t3e18 11518 6t5e30 11520 5recm6rec 11562 bpoly2 14627 bpoly3 14628 bpoly4 14629 efi4p 14706 ef01bndlem 14753 cos01bnd 14755 3lcm2e6woprm 15166 6lcm4e12 15167 2exp8 15634 2exp16 15635 19prm 15663 83prm 15668 163prm 15670 317prm 15671 631prm 15672 prmo6 15675 1259lem1 15676 1259lem2 15677 1259lem3 15678 1259lem4 15679 1259lem5 15680 2503lem1 15682 2503lem2 15683 2503lem3 15684 2503prm 15685 4001lem1 15686 4001lem2 15687 4001lem4 15689 4001prm 15690 sincos6thpi 24071 sincos3rdpi 24072 1cubrlem 24368 log2ublem3 24475 log2ub 24476 basellem5 24611 basellem8 24614 ppiub 24729 bclbnd 24805 bposlem8 24816 bposlem9 24817 2lgslem3d 24924 2lgsoddprmlem3d 24938 ex-exp 26699 ex-bc 26701 ex-gcd 26706 ex-lcm 26707 problem5 30817 lhe4.4ex1a 37550 wallispi2lem2 38965 fmtno5lem1 40003 fmtno5lem4 40006 fmtno5 40007 fmtno4prmfac 40022 fmtno5faclem2 40030 fmtno5faclem3 40031 fmtno5fac 40032 flsqrt5 40047 139prmALT 40049 127prm 40053 2exp11 40055 mod42tp1mod8 40057 2t6m3t4e0 41919 zlmodzxzequa 42079 zlmodzxzequap 42082 |
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