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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 6095 and dfrel3 6104. (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 5593 | . 2 wff Rel 𝐴 |
3 | cvv 3431 | . . . 4 class V | |
4 | 3, 3 | cxp 5586 | . . 3 class (V × V) |
5 | 1, 4 | wss 3886 | . 2 wff 𝐴 ⊆ (V × V) |
6 | 2, 5 | wb 205 | 1 wff (Rel 𝐴 ↔ 𝐴 ⊆ (V × V)) |
Colors of variables: wff setvar class |
This definition is referenced by: relxp 5606 pwvrel 5636 brrelex12 5638 0nelrel0 5646 releq 5686 nfrel 5689 sbcrel 5690 relss 5691 ssrel 5692 ssrelOLD 5693 elrel 5708 rel0 5709 nrelv 5710 relsng 5711 relun 5721 reliun 5726 reliin 5727 relopabiv 5730 relopabi 5732 relopabiALT 5733 exopxfr2 5754 relop 5760 eqbrrdva 5779 elreldm 5845 cnvcnv 6098 relrelss 6178 cnviin 6191 dff3 6983 oprabss 7388 relmptopab 7526 1st2nd 7887 1stdm 7888 releldm2 7891 relmpoopab 7941 reldmtpos 8057 dmtpos 8061 dftpos4 8068 tpostpos 8069 iiner 8585 fundmen 8828 nqerf 10693 uzrdgfni 13685 hashfun 14159 reltrclfv 14735 homarel 17758 relxpchom 17905 ustrel 23370 utop2nei 23409 utop3cls 23410 metustrel 23715 pi1xfrcnv 24227 reldv 25041 dvbsss 25073 ssrelf 30962 1stpreimas 31045 fpwrelmap 31075 gsumhashmul 31323 metideq 31850 metider 31851 pstmfval 31853 esum2d 32068 txprel 34188 relsset 34197 elfuns 34224 fnsingle 34228 funimage 34237 bj-opelrelex 35322 bj-elid5 35347 mblfinlem1 35821 rngosn3 36089 xrnrel 36508 elrelsrel 36610 dihvalrel 39298 cnvcnvintabd 41213 cnvintabd 41216 clcnvlem 41236 rfovcnvf1od 41617 relopabVD 42526 sprsymrelfo 44970 |
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