Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 4594 | . 2 | |
2 | 1 | relopabi 4712 | 1 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 3965 ccnv 4585 wrel 4591 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-opab 4026 df-xp 4592 df-rel 4593 df-cnv 4594 |
This theorem is referenced by: relbrcnvg 4965 cnvsym 4969 intasym 4970 asymref 4971 cnvopab 4987 cnv0 4989 cnvdif 4992 dfrel2 5036 cnvcnv 5038 cnvsn0 5054 cnvcnvsn 5062 resdm2 5076 coi2 5102 coires1 5103 cnvssrndm 5107 unidmrn 5118 cnvexg 5123 cnviinm 5127 funi 5202 funcnvsn 5215 funcnv2 5230 funcnveq 5233 fcnvres 5353 f1cnvcnv 5386 f1ompt 5618 fliftcnv 5745 cnvf1o 6172 reldmtpos 6200 dmtpos 6203 rntpos 6204 dftpos3 6209 dftpos4 6210 tpostpos 6211 tposf12 6216 ercnv 6501 cnvct 6754 relcnvfi 6885 fsumcnv 11334 fisumcom2 11335 fprodcnv 11522 fprodcom2fi 11523 |
Copyright terms: Public domain | W3C validator |