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Mirrors > Home > ILE Home > Th. List > brcnv | Unicode version |
Description: The converse of a binary relation swaps arguments. Theorem 11 of [Suppes] p. 61. (Contributed by NM, 13-Aug-1995.) |
Ref | Expression |
---|---|
opelcnv.1 |
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opelcnv.2 |
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Ref | Expression |
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brcnv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelcnv.1 |
. 2
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2 | opelcnv.2 |
. 2
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3 | brcnvg 4459 |
. 2
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4 | 1, 2, 3 | mp2an 402 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-pow 3918 ax-pr 3935 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 df-un 2916 df-in 2918 df-ss 2925 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-br 3756 df-opab 3810 df-cnv 4296 |
This theorem is referenced by: cnvco 4463 dfrn2 4466 dfdm4 4470 cnvsym 4651 intasym 4652 asymref 4653 qfto 4657 dminss 4681 imainss 4682 dminxp 4708 cnvcnv3 4713 cnvpom 4803 cnvsom 4804 dffun2 4855 funcnvsn 4888 funcnv2 4902 funcnveq 4905 fun2cnv 4906 imadif 4922 f1ompt 5263 f1eqcocnv 5374 fliftcnv 5378 isocnv2 5395 ercnv 6063 ecid 6105 |
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