Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > opelstrsl | Unicode version |
Description: The slot of a structure which contains an ordered pair for that slot. (Contributed by Jim Kingdon, 5-Feb-2023.) |
Ref | Expression |
---|---|
opelstrsl.e | Slot |
opelstrsl.s | Struct |
opelstrsl.v | |
opelstrsl.el |
Ref | Expression |
---|---|
opelstrsl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelstrsl.e | . 2 Slot | |
2 | opelstrsl.s | . . 3 Struct | |
3 | structex 11898 | . . 3 Struct | |
4 | 2, 3 | syl 14 | . 2 |
5 | structfung 11903 | . . 3 Struct | |
6 | 2, 5 | syl 14 | . 2 |
7 | opelstrsl.el | . 2 | |
8 | opelstrsl.v | . 2 | |
9 | 1, 4, 6, 7, 8 | strslfv2d 11928 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wcel 1465 cvv 2660 cop 3500 class class class wbr 3899 ccnv 4508 wfun 5087 cfv 5093 cn 8688 Struct cstr 11882 cnx 11883 Slot cslot 11885 |
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-in1 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-sbc 2883 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-iota 5058 df-fun 5095 df-fv 5101 df-struct 11888 df-slot 11890 |
This theorem is referenced by: opelstrbas 11983 2strop1g 11991 rngplusgg 12003 rngmulrg 12004 srngplusgd 12010 srngmulrd 12011 srnginvld 12012 lmodplusgd 12021 lmodscad 12022 lmodvscad 12023 ipsaddgd 12029 ipsmulrd 12030 ipsscad 12031 ipsvscad 12032 ipsipd 12033 topgrpplusgd 12039 topgrptsetd 12040 |
Copyright terms: Public domain | W3C validator |