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Mirrors > Home > MPE Home > Th. List > mndmgm | Structured version Visualization version Unicode version |
Description: A monoid is a magma. (Contributed by FL, 2-Nov-2009.) (Revised by AV, 6-Jan-2020.) (Proof shortened by AV, 6-Feb-2020.) |
Ref | Expression |
---|---|
mndmgm | Mgm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mndsgrp 17299 | . 2 SGrp | |
2 | sgrpmgm 17289 | . 2 SGrp Mgm | |
3 | 1, 2 | syl 17 | 1 Mgm |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 Mgmcmgm 17240 SGrpcsgrp 17283 cmnd 17294 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-nul 4789 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-ov 6653 df-sgrp 17284 df-mnd 17295 |
This theorem is referenced by: mndcl 17301 mndplusf 17309 srg1zr 18529 ringmgm 18557 chfacfpmmulgsum2 20670 cayhamlem1 20671 ofldchr 29814 idomrootle 37773 ismhm0 41805 mhmismgmhm 41806 c0mgm 41909 c0snmgmhm 41914 c0snmhm 41915 |
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