Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 12155 | . 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 7627 cxr 7806 clt 7807 cnx 11966 cbs 11969 cplusg 12031 cmulr 12032 Scalarcsca 12034 cvsca 12035 cip 12036 TopSetcts 12037 cple 12038 cds 12040 chom 12042 compcco 12043 ctopn 12131 cpt 12146 g cgsu 12148 scprds 12153 |
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 12155 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |