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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 4521 | . . 3 | |
2 | inss2 3267 | . . 3 | |
3 | 1, 2 | eqsstri 3099 | . 2 |
4 | relxp 4618 | . 2 | |
5 | relss 4596 | . 2 | |
6 | 3, 4, 5 | mp2 16 | 1 |
Colors of variables: wff set class |
Syntax hints: cvv 2660 cin 3040 wss 3041 cxp 4507 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-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-in 3047 df-ss 3054 df-opab 3960 df-xp 4515 df-rel 4516 df-res 4521 |
This theorem is referenced by: elres 4825 resiexg 4834 iss 4835 dfres2 4841 issref 4891 asymref 4894 poirr2 4901 cnvcnvres 4972 resco 5013 ressn 5049 funssres 5135 fnresdisj 5203 fnres 5209 fcnvres 5276 nfunsn 5423 fsnunfv 5589 resfunexgALT 5976 setsresg 11908 |
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