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Mirrors > Home > ILE Home > Th. List > resindm | Unicode version |
Description: When restricting a relation, intersecting with the domain of the relation has no effect. (Contributed by FL, 6-Oct-2008.) |
Ref | Expression |
---|---|
resindm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resdm 4828 | . . 3 | |
2 | 1 | ineq2d 3247 | . 2 |
3 | resindi 4804 | . 2 | |
4 | incom 3238 | . . 3 | |
5 | inres 4806 | . . 3 | |
6 | inidm 3255 | . . . 4 | |
7 | 6 | reseq1i 4785 | . . 3 |
8 | 4, 5, 7 | 3eqtrri 2143 | . 2 |
9 | 2, 3, 8 | 3eqtr4g 2175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 cin 3040 cdm 4509 cres 4511 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-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-dm 4519 df-res 4521 |
This theorem is referenced by: resdmdfsn 4832 |
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