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Mirrors > Home > ILE Home > Th. List > brcnvg | Unicode version |
Description: The converse of a binary relation swaps arguments. Theorem 11 of [Suppes] p. 61. (Contributed by NM, 10-Oct-2005.) |
Ref | Expression |
---|---|
brcnvg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelcnvg 4533 | . 2 | |
2 | df-br 3786 | . 2 | |
3 | df-br 3786 | . 2 | |
4 | 1, 2, 3 | 3bitr4g 221 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wcel 1433 cop 3401 class class class wbr 3785 ccnv 4362 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-opab 3840 df-cnv 4371 |
This theorem is referenced by: brcnv 4536 brelrng 4583 eliniseg 4715 relbrcnvg 4724 brcodir 4732 sefvex 5216 foeqcnvco 5450 isocnv2 5472 ersym 6141 brdifun 6156 ecidg 6193 cnvti 6432 eqinfti 6433 inflbti 6437 infglbti 6438 negiso 8033 |
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