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Mirrors > Home > ILE Home > Th. List > relcnv | Unicode version |
Description: A converse is a relation. Theorem 12 of [Suppes] p. 62. (Contributed by NM, 29-Oct-1996.) |
Ref | Expression |
---|---|
relcnv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-cnv 4547 | . 2 | |
2 | 1 | relopabi 4665 | 1 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 3929 ccnv 4538 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-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-opab 3990 df-xp 4545 df-rel 4546 df-cnv 4547 |
This theorem is referenced by: relbrcnvg 4918 cnvsym 4922 intasym 4923 asymref 4924 cnvopab 4940 cnv0 4942 cnvdif 4945 dfrel2 4989 cnvcnv 4991 cnvsn0 5007 cnvcnvsn 5015 resdm2 5029 coi2 5055 coires1 5056 cnvssrndm 5060 unidmrn 5071 cnvexg 5076 cnviinm 5080 funi 5155 funcnvsn 5168 funcnv2 5183 funcnveq 5186 fcnvres 5306 f1cnvcnv 5339 f1ompt 5571 fliftcnv 5696 cnvf1o 6122 reldmtpos 6150 dmtpos 6153 rntpos 6154 dftpos3 6159 dftpos4 6160 tpostpos 6161 tposf12 6166 ercnv 6450 cnvct 6703 relcnvfi 6829 fsumcnv 11206 fisumcom2 11207 |
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