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Mirrors > Home > ILE Home > Th. List > isstructr | 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 |
---|---|
isstructr | Struct |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brinxp2 4678 | . . . 4 | |
2 | df-br 3990 | . . . 4 | |
3 | 1, 2 | sylbb1 136 | . . 3 |
4 | 3 | adantr 274 | . 2 |
5 | simpr1 998 | . 2 | |
6 | simpr2 999 | . 2 | |
7 | df-ov 5856 | . . . . . 6 | |
8 | 7 | sseq2i 3174 | . . . . 5 |
9 | 8 | biimpi 119 | . . . 4 |
10 | 9 | 3ad2ant3 1015 | . . 3 |
11 | 10 | adantl 275 | . 2 |
12 | isstruct2r 12427 | . 2 Struct | |
13 | 4, 5, 6, 11, 12 | syl22anc 1234 | 1 Struct |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 973 wcel 2141 cdif 3118 cin 3120 wss 3121 c0 3414 csn 3583 cop 3586 class class class wbr 3989 cxp 4609 cdm 4611 wfun 5192 cfv 5198 (class class class)co 5853 cle 7955 cn 8878 cfz 9965 Struct cstr 12412 |
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-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
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-dif 3123 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-br 3990 df-opab 4051 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-iota 5160 df-fun 5200 df-fv 5206 df-ov 5856 df-struct 12418 |
This theorem is referenced by: strleund 12506 strleun 12507 strle1g 12508 |
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