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Mirrors > Home > ILE Home > Th. List > isstructim | Unicode version |
Description: The property of being a structure with components in . (Contributed by Mario Carneiro, 29-Aug-2015.) (Revised by Jim Kingdon, 18-Jan-2023.) |
Ref | Expression |
---|---|
isstructim | Struct |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isstruct2im 12347 | . 2 Struct | |
2 | brinxp2 4665 | . . . 4 | |
3 | df-br 3977 | . . . 4 | |
4 | 2, 3 | bitr3i 185 | . . 3 |
5 | biid 170 | . . 3 | |
6 | df-ov 5839 | . . . 4 | |
7 | 6 | sseq2i 3164 | . . 3 |
8 | 4, 5, 7 | 3anbi123i 1177 | . 2 |
9 | 1, 8 | sylibr 133 | 1 Struct |
Colors of variables: wff set class |
Syntax hints: wi 4 w3a 967 wcel 2135 cdif 3108 cin 3110 wss 3111 c0 3404 csn 3570 cop 3573 class class class wbr 3976 cxp 4596 cdm 4598 wfun 5176 cfv 5182 (class class class)co 5836 cle 7925 cn 8848 cfz 9935 Struct cstr 12333 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-iota 5147 df-fun 5184 df-fv 5190 df-ov 5839 df-struct 12339 |
This theorem is referenced by: structfn 12356 strsetsid 12370 strleund 12425 strleun 12426 |
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