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Mirrors > Home > ILE Home > Th. List > breqtrrdi | Unicode version |
Description: A chained equality inference for a binary relation. (Contributed by NM, 24-Apr-2005.) |
Ref | Expression |
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breqtrrdi.1 |
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breqtrrdi.2 |
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Ref | Expression |
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breqtrrdi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breqtrrdi.1 |
. 2
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2 | breqtrrdi.2 |
. . 3
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3 | 2 | eqcomi 2144 |
. 2
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4 | 1, 3 | breqtrdi 3977 |
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-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 |
This theorem is referenced by: enpr2d 6719 fiunsnnn 6783 unsnfi 6815 eninl 6990 eninr 6991 difinfinf 6994 exmidfodomrlemr 7075 exmidfodomrlemrALT 7076 dju1en 7086 djucomen 7089 djuassen 7090 xpdjuen 7091 gtndiv 9170 intqfrac2 10123 uzenom 10229 xrmaxiflemval 11051 ege2le3 11414 eirraplem 11519 2strstr1g 12101 lmcn2 12488 dveflem 12895 tangtx 12967 ioocosf1o 12983 sbthom 13396 |
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