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Mirrors > Home > MPE Home > Th. List > df-rel | Structured version Visualization version GIF version |
Description: Define the relation predicate. Definition 6.4(1) of [TakeutiZaring] p. 23. For alternate definitions, see dfrel2 6210 and dfrel3 6219. (Contributed by NM, 1-Aug-1994.) |
Ref | Expression |
---|---|
df-rel | ⊢ (Rel 𝐴 ↔ 𝐴 ⊆ (V × V)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | 1 | wrel 5693 | . 2 wff Rel 𝐴 |
3 | cvv 3477 | . . . 4 class V | |
4 | 3, 3 | cxp 5686 | . . 3 class (V × V) |
5 | 1, 4 | wss 3962 | . 2 wff 𝐴 ⊆ (V × V) |
6 | 2, 5 | wb 206 | 1 wff (Rel 𝐴 ↔ 𝐴 ⊆ (V × V)) |
Colors of variables: wff setvar class |
This definition is referenced by: relxp 5706 pwvrel 5738 brrelex12 5740 0nelrel0 5748 releq 5788 nfrel 5791 sbcrel 5792 relss 5793 ssrel 5794 ssrelOLD 5795 elrel 5810 rel0 5811 nrelv 5812 relsng 5813 relun 5823 reliun 5828 reliin 5829 relopabiv 5832 relopabi 5834 relopabiALT 5835 exopxfr2 5857 relop 5863 eqbrrdva 5882 elreldm 5948 cnvcnv 6213 relrelss 6294 cnviin 6307 dff3 7119 oprabss 7539 relmptopab 7682 1st2nd 8062 1stdm 8063 releldm2 8066 relmpoopab 8117 reldmtpos 8257 dmtpos 8261 dftpos4 8268 tpostpos 8269 iiner 8827 fundmen 9069 nqerf 10967 uzrdgfni 13995 hashfun 14472 reltrclfv 15052 homarel 18089 relxpchom 18236 ustrel 24235 utop2nei 24274 utop3cls 24275 metustrel 24580 pi1xfrcnv 25103 reldv 25919 dvbsss 25951 ssrelf 32634 1stpreimas 32720 fpwrelmap 32750 gsumhashmul 33046 metideq 33853 metider 33854 pstmfval 33856 esum2d 34073 txprel 35860 relsset 35869 elfuns 35896 fnsingle 35900 funimage 35909 bj-opelrelex 37126 bj-elid5 37151 mblfinlem1 37643 rngosn3 37910 xrnrel 38354 elrelsrel 38468 dihvalrel 41261 cnvcnvintabd 43589 cnvintabd 43592 clcnvlem 43612 rfovcnvf1od 43993 relopabVD 44898 sprsymrelfo 47421 |
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