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Mirrors > Home > ILE Home > Th. List > relres | Unicode version |
Description: A restriction is a relation. Exercise 12 of [TakeutiZaring] p. 25. (Contributed by NM, 2-Aug-1994.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
relres |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-res 4551 | . . 3 | |
2 | inss2 3297 | . . 3 | |
3 | 1, 2 | eqsstri 3129 | . 2 |
4 | relxp 4648 | . 2 | |
5 | relss 4626 | . 2 | |
6 | 3, 4, 5 | mp2 16 | 1 |
Colors of variables: wff set class |
Syntax hints: cvv 2686 cin 3070 wss 3071 cxp 4537 cres 4541 wrel 4544 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-in 3077 df-ss 3084 df-opab 3990 df-xp 4545 df-rel 4546 df-res 4551 |
This theorem is referenced by: elres 4855 resiexg 4864 iss 4865 dfres2 4871 issref 4921 asymref 4924 poirr2 4931 cnvcnvres 5002 resco 5043 ressn 5079 funssres 5165 fnresdisj 5233 fnres 5239 fcnvres 5306 nfunsn 5455 fsnunfv 5621 resfunexgALT 6008 setsresg 11997 |
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