Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > reldmprds | Structured version Visualization version 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 16108 | . 2 s Scalar g TopSet comp comp | |
2 | 1 | reldmmpt2 6771 | 1 s |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wral 2912 cvv 3200 csb 3533 cun 3572 wss 3574 csn 4177 cpr 4179 ctp 4181 cop 4183 class class class wbr 4653 copab 4712 cmpt 4729 cxp 5112 cdm 5114 crn 5115 ccom 5118 wrel 5119 cfv 5888 (class class class)co 6650 cmpt2 6652 c1st 7166 c2nd 7167 cixp 7908 csup 8346 cc0 9936 cxr 10073 clt 10074 cnx 15854 cbs 15857 cplusg 15941 cmulr 15942 Scalarcsca 15944 cvsca 15945 cip 15946 TopSetcts 15947 cple 15948 cds 15950 chom 15952 compcco 15953 ctopn 16082 cpt 16099 g cgsu 16101 scprds 16106 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-xp 5120 df-rel 5121 df-dm 5124 df-oprab 6654 df-mpt2 6655 df-prds 16108 |
This theorem is referenced by: dsmmval 20078 dsmmval2 20080 dsmmbas2 20081 dsmmfi 20082 |
Copyright terms: Public domain | W3C validator |