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Mirrors > Home > MPE Home > Th. List > 8cn | Structured version Visualization version GIF version |
Description: The number 8 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
8cn | ⊢ 8 ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 8re 10982 | . 2 ⊢ 8 ∈ ℝ | |
2 | 1 | recni 9931 | 1 ⊢ 8 ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1977 ℂcc 9813 8c8 10953 |
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 df-7 10961 df-8 10962 |
This theorem is referenced by: 9m1e8 11020 8p2e10OLD 11051 8p2e10 11486 8t2e16 11530 8t5e40 11533 8t5e40OLD 11534 cos2bnd 14757 2exp16 15635 139prm 15669 163prm 15670 317prm 15671 631prm 15672 1259lem2 15677 1259lem3 15678 1259lem4 15679 1259lem5 15680 2503lem2 15683 2503lem3 15684 2503prm 15685 4001lem1 15686 4001lem2 15687 4001prm 15690 quart1cl 24381 quart1lem 24382 quart1 24383 quartlem1 24384 log2tlbnd 24472 log2ublem3 24475 log2ub 24476 bposlem8 24816 lgsdir2lem1 24850 lgsdir2lem3 24852 lgsdir2lem5 24854 2lgslem3a 24921 2lgslem3b 24922 2lgslem3c 24923 2lgslem3d 24924 2lgslem3a1 24925 2lgslem3b1 24926 2lgslem3c1 24927 2lgslem3d1 24928 2lgsoddprmlem1 24933 2lgsoddprmlem2 24934 2lgsoddprmlem3a 24935 2lgsoddprmlem3b 24936 2lgsoddprmlem3c 24937 2lgsoddprmlem3d 24938 ex-exp 26699 fmtno5lem4 40006 257prm 40011 fmtnoprmfac2lem1 40016 fmtno4prmfac 40022 fmtno4nprmfac193 40024 fmtno5faclem3 40031 m3prm 40044 139prmALT 40049 127prm 40053 m7prm 40054 2exp11 40055 5tcu2e40 40070 evengpop3 40214 tgoldbachlt 40230 tgoldbachltOLD 40237 |
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