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Mirrors > Home > MPE Home > Th. List > drnggrp | Structured version Visualization version Unicode version |
Description: A division ring is a group. (Contributed by NM, 8-Sep-2011.) |
Ref | Expression |
---|---|
drnggrp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | drngring 17975 |
. 2
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2 | ringgrp 17778 |
. 2
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3 | 1, 2 | syl 17 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 ax-nul 4533 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 986 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-eu 2302 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ne 2623 df-ral 2741 df-rex 2742 df-rab 2745 df-v 3046 df-sbc 3267 df-dif 3406 df-un 3408 df-in 3410 df-ss 3417 df-nul 3731 df-if 3881 df-sn 3968 df-pr 3970 df-op 3974 df-uni 4198 df-br 4402 df-iota 5545 df-fv 5589 df-ov 6291 df-ring 17775 df-drng 17970 |
This theorem is referenced by: qqh0 28781 qqhghm 28785 dvhvaddass 34659 dvhgrp 34669 cdlemn4 34760 |
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