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Mirrors > Home > ILE Home > Th. List > reldmprds | Unicode version |
Description: The structure product is a well-behaved binary operator. (Contributed by Stefan O'Rear, 7-Jan-2015.) (Revised by Thierry Arnoux, 15-Jun-2019.) |
Ref | Expression |
---|---|
reldmprds | s |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-prds 12145 | . 2 s Scalar g TopSet comp comp | |
2 | 1 | reldmmpo 5882 | 1 s |
Colors of variables: wff set class |
Syntax hints: wa 103 wral 2416 cvv 2686 csb 3003 cun 3069 wss 3071 csn 3527 cpr 3528 ctp 3529 cop 3530 class class class wbr 3929 copab 3988 cmpt 3989 cxp 4537 cdm 4539 crn 4540 ccom 4543 wrel 4544 cfv 5123 (class class class)co 5774 cmpo 5776 c1st 6036 c2nd 6037 cixp 6592 csup 6869 cc0 7620 cxr 7799 clt 7800 cnx 11956 cbs 11959 cplusg 12021 cmulr 12022 Scalarcsca 12024 cvsca 12025 cip 12026 TopSetcts 12027 cple 12028 cds 12030 chom 12032 compcco 12033 ctopn 12121 cpt 12136 g cgsu 12138 scprds 12143 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-xp 4545 df-rel 4546 df-dm 4549 df-oprab 5778 df-mpo 5779 df-prds 12145 |
This theorem is referenced by: (None) |
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