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Mirrors > Home > MPE Home > Th. List > iscyg2 | Structured version Visualization version Unicode version |
Description: A cyclic group is a group which contains a generator. (Contributed by Mario Carneiro, 21-Apr-2016.) |
Ref | Expression |
---|---|
iscyg.1 |
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iscyg.2 |
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iscyg3.e |
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Ref | Expression |
---|---|
iscyg2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iscyg.1 |
. . 3
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2 | iscyg.2 |
. . 3
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3 | 1, 2 | iscyg 17563 |
. 2
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4 | iscyg3.e |
. . . . 5
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5 | 4 | neeq1i 2700 |
. . . 4
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6 | rabn0 3764 |
. . . 4
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7 | 5, 6 | bitri 257 |
. . 3
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8 | 7 | anbi2i 705 |
. 2
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9 | 3, 8 | bitr4i 260 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-rab 2758 df-v 3059 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4213 df-br 4417 df-opab 4476 df-mpt 4477 df-cnv 4861 df-dm 4863 df-rn 4864 df-iota 5565 df-fv 5609 df-ov 6318 df-cyg 17562 |
This theorem is referenced by: iscygd 17571 iscygodd 17572 cyggex2 17580 cyggexb 17582 cygzn 19190 |
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