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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 4719 | . 2 | |
2 | df-br 3930 | . 2 | |
3 | df-br 3930 | . 2 | |
4 | 1, 2, 3 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wcel 1480 cop 3530 class class class wbr 3929 ccnv 4538 |
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-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 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-br 3930 df-opab 3990 df-cnv 4547 |
This theorem is referenced by: brcnv 4722 brelrng 4770 eliniseg 4909 relbrcnvg 4918 brcodir 4926 sefvex 5442 foeqcnvco 5691 isocnv2 5713 ersym 6441 brdifun 6456 ecidg 6493 cnvti 6906 eqinfti 6907 inflbti 6911 infglbti 6912 negiso 8713 xrnegiso 11031 |
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