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Mirrors > Home > ILE Home > Th. List > relssdmrn | Unicode version |
Description: A relation is included in the cross product of its domain and range. Exercise 4.12(t) of [Mendelson] p. 235. (Contributed by NM, 3-Aug-1994.) |
Ref | Expression |
---|---|
relssdmrn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 | |
2 | 19.8a 1554 | . . . 4 | |
3 | 19.8a 1554 | . . . 4 | |
4 | opelxp 4539 | . . . . 5 | |
5 | vex 2663 | . . . . . . 7 | |
6 | 5 | eldm2 4707 | . . . . . 6 |
7 | vex 2663 | . . . . . . 7 | |
8 | 7 | elrn2 4751 | . . . . . 6 |
9 | 6, 8 | anbi12i 455 | . . . . 5 |
10 | 4, 9 | bitri 183 | . . . 4 |
11 | 2, 3, 10 | sylanbrc 413 | . . 3 |
12 | 11 | a1i 9 | . 2 |
13 | 1, 12 | relssdv 4601 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1453 wcel 1465 wss 3041 cop 3500 cxp 4507 cdm 4509 crn 4510 wrel 4514 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-xp 4515 df-rel 4516 df-cnv 4517 df-dm 4519 df-rn 4520 |
This theorem is referenced by: cnvssrndm 5030 cossxp 5031 relrelss 5035 relfld 5037 cnvexg 5046 fssxp 5260 oprabss 5825 resfunexgALT 5976 cofunexg 5977 fnexALT 5979 erssxp 6420 |
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