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Mirrors > Home > ILE Home > Th. List > sgrpmgm | Unicode version |
Description: A semigroup is a magma. (Contributed by FL, 2-Nov-2009.) (Revised by AV, 6-Jan-2020.) |
Ref | Expression |
---|---|
sgrpmgm | Smgrp Mgm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2170 | . . 3 | |
2 | eqid 2170 | . . 3 | |
3 | 1, 2 | issgrp 12644 | . 2 Smgrp Mgm |
4 | 3 | simplbi 272 | 1 Smgrp Mgm |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wcel 2141 wral 2448 cfv 5198 (class class class)co 5853 cbs 12416 cplusg 12480 Mgmcmgm 12608 Smgrpcsgrp 12642 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 ax-un 4418 ax-cnex 7865 ax-resscn 7866 ax-1re 7868 ax-addrcl 7871 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-sbc 2956 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-int 3832 df-br 3990 df-opab 4051 df-mpt 4052 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-rn 4622 df-res 4623 df-iota 5160 df-fun 5200 df-fn 5201 df-fv 5206 df-ov 5856 df-inn 8879 df-2 8937 df-ndx 12419 df-slot 12420 df-base 12422 df-plusg 12493 df-sgrp 12643 |
This theorem is referenced by: mndmgm 12658 dfgrp2 12732 |
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