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Mirrors > Home > ILE Home > Th. List > eqbrtrdi | Unicode version |
Description: A chained equality inference for a binary relation. (Contributed by NM, 12-Oct-1999.) |
Ref | Expression |
---|---|
eqbrtrdi.1 |
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eqbrtrdi.2 |
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Ref | Expression |
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eqbrtrdi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqbrtrdi.2 |
. 2
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2 | eqbrtrdi.1 |
. . 3
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3 | 2 | breq1d 4025 |
. 2
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4 | 1, 3 | mpbiri 168 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-v 2751 df-un 3145 df-sn 3610 df-pr 3611 df-op 3613 df-br 4016 |
This theorem is referenced by: eqbrtrrdi 4055 pm54.43 7202 recapb 8641 nn0ledivnn 9780 xltnegi 9848 leexp1a 10588 facwordi 10733 faclbnd3 10736 resqrexlemlo 11035 efap0 11698 dvds1 11872 en1top 13848 dvef 14459 rpabscxpbnd 14630 zabsle1 14671 trirec0 15064 |
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