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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 4619 | . 2 | |
2 | 1 | relopabi 4737 | 1 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 3989 ccnv 4610 wrel 4616 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-opab 4051 df-xp 4617 df-rel 4618 df-cnv 4619 |
This theorem is referenced by: relbrcnvg 4990 cnvsym 4994 intasym 4995 asymref 4996 cnvopab 5012 cnv0 5014 cnvdif 5017 dfrel2 5061 cnvcnv 5063 cnvsn0 5079 cnvcnvsn 5087 resdm2 5101 coi2 5127 coires1 5128 cnvssrndm 5132 unidmrn 5143 cnvexg 5148 cnviinm 5152 funi 5230 funcnvsn 5243 funcnv2 5258 funcnveq 5261 fcnvres 5381 f1cnvcnv 5414 f1ompt 5647 fliftcnv 5774 cnvf1o 6204 reldmtpos 6232 dmtpos 6235 rntpos 6236 dftpos3 6241 dftpos4 6242 tpostpos 6243 tposf12 6248 ercnv 6534 cnvct 6787 relcnvfi 6918 fsumcnv 11400 fisumcom2 11401 fprodcnv 11588 fprodcom2fi 11589 |
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