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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 4728 |
. 2
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4 | 1, 2, 3 | mp2an 423 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-opab 3998 df-cnv 4555 |
This theorem is referenced by: cnvco 4732 dfrn2 4735 dfdm4 4739 cnvsym 4930 intasym 4931 asymref 4932 qfto 4936 dminss 4961 imainss 4962 dminxp 4991 cnvcnv3 4996 cnvpom 5089 cnvsom 5090 dffun2 5141 funcnvsn 5176 funcnv2 5191 funcnveq 5194 fun2cnv 5195 imadif 5211 f1ompt 5579 f1eqcocnv 5700 fliftcnv 5704 isocnv2 5721 ercnv 6458 ecid 6500 cnvinfex 6913 eqinfti 6915 infvalti 6917 infmoti 6923 dfinfre 8738 pw1nct 13371 |
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