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| Mirrors > Home > ILE Home > Th. List > plusgslid | Unicode version | ||
| Description: Slot property of |
| Ref | Expression |
|---|---|
| plusgslid |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-plusg 12893 |
. 2
| |
| 2 | 2nn 9197 |
. 2
| |
| 3 | 1, 2 | ndxslid 12828 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-13 2177 ax-14 2178 ax-ext 2186 ax-sep 4161 ax-pow 4217 ax-pr 4252 ax-un 4479 ax-cnex 8015 ax-resscn 8016 ax-1re 8018 ax-addrcl 8021 |
| This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1375 df-nf 1483 df-sb 1785 df-eu 2056 df-mo 2057 df-clab 2191 df-cleq 2197 df-clel 2200 df-nfc 2336 df-ral 2488 df-rex 2489 df-v 2773 df-sbc 2998 df-un 3169 df-in 3171 df-ss 3178 df-pw 3617 df-sn 3638 df-pr 3639 df-op 3641 df-uni 3850 df-int 3885 df-br 4044 df-opab 4105 df-mpt 4106 df-id 4339 df-xp 4680 df-rel 4681 df-cnv 4682 df-co 4683 df-dm 4684 df-rn 4685 df-res 4686 df-iota 5231 df-fun 5272 df-fv 5278 df-ov 5946 df-inn 9036 df-2 9094 df-ndx 12806 df-slot 12807 df-plusg 12893 |
| This theorem is referenced by: ressplusgd 12932 rngplusgg 12940 srngplusgd 12951 lmodplusgd 12969 ipsaddgd 12981 topgrpplusgd 13001 prdsplusgfval 13087 imasex 13108 imasival 13109 imasbas 13110 imasplusg 13111 imasaddfn 13120 imasaddval 13121 imasaddf 13122 qusaddval 13138 qusaddf 13139 ismgm 13160 plusfvalg 13166 plusffng 13168 gsumpropd2 13196 gsumsplit1r 13201 gsumprval 13202 issgrp 13206 ismnddef 13221 gsumfzz 13298 gsumwsubmcl 13299 gsumwmhm 13301 gsumfzcl 13302 grppropstrg 13322 grpsubval 13349 mulgval 13429 mulgfng 13431 mulgnngsum 13434 mulg1 13436 mulgnnp1 13437 mulgnndir 13458 subgintm 13505 isnsg 13509 gsumfzreidx 13644 gsumfzsubmcl 13645 gsumfzmptfidmadd 13646 gsumfzconst 13648 gsumfzmhm 13650 fnmgp 13655 mgpvalg 13656 mgpplusgg 13657 mgpex 13658 mgpbasg 13659 mgpscag 13660 mgptsetg 13661 mgpdsg 13663 mgpress 13664 isrng 13667 issrg 13698 isring 13733 ring1 13792 oppraddg 13809 islmod 14024 rmodislmod 14084 lsssn0 14103 lss1d 14116 lssintclm 14117 sraaddgg 14173 mpocnfldadd 14294 psrplusgg 14411 |
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