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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 | |
eqbrtrdi.2 |
Ref | Expression |
---|---|
eqbrtrdi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqbrtrdi.2 | . 2 | |
2 | eqbrtrdi.1 | . . 3 | |
3 | 2 | breq1d 3939 | . 2 |
4 | 1, 3 | mpbiri 167 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 class class class wbr 3929 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 |
This theorem is referenced by: eqbrtrrdi 3968 pm54.43 7046 nn0ledivnn 9554 xltnegi 9618 leexp1a 10348 facwordi 10486 faclbnd3 10489 resqrexlemlo 10785 efap0 11383 dvds1 11551 en1top 12246 dvef 12856 |
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