Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > brxp | Structured version Visualization version Unicode version |
Description: Binary relation on a Cartesian product. (Contributed by NM, 22-Apr-2004.) |
Ref | Expression |
---|---|
brxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 4654 | . 2 | |
2 | opelxp 5146 | . 2 | |
3 | 1, 2 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wcel 1990 cop 4183 class class class wbr 4653 cxp 5112 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 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 |
This theorem is referenced by: brrelex12 5155 brel 5168 brinxp2 5180 eqbrrdva 5291 ssrelrn 5315 xpidtr 5518 xpco 5675 isocnv3 6582 tpostpos 7372 swoer 7772 erinxp 7821 ecopover 7851 ecopoverOLD 7852 infxpenlem 8836 fpwwe2lem6 9457 fpwwe2lem7 9458 fpwwe2lem9 9460 fpwwe2lem12 9463 fpwwe2lem13 9464 fpwwe2 9465 ltxrlt 10108 ltxr 11949 xpcogend 13713 xpsfrnel2 16225 invfuc 16634 elhoma 16682 efglem 18129 gsumdixp 18609 gsumbagdiag 19376 psrass1lem 19377 opsrtoslem2 19485 znleval 19903 gsumcom3fi 20206 brelg 29421 posrasymb 29657 trleile 29666 metider 29937 mclsppslem 31480 dfpo2 31645 slenlt 31877 dfon3 31999 brbigcup 32005 brsingle 32024 brimage 32033 brcart 32039 brapply 32045 brcup 32046 brcap 32047 funpartlem 32049 dfrdg4 32058 brub 32061 itg2gt0cn 33465 brinxp2ALTV 34034 |
Copyright terms: Public domain | W3C validator |