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Mirrors > Home > ILE Home > Th. List > eqbrtri | Unicode version |
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eqbrtr.1 | |
eqbrtr.2 |
Ref | Expression |
---|---|
eqbrtri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqbrtr.2 | . 2 | |
2 | eqbrtr.1 | . . 3 | |
3 | 2 | breq1i 3983 | . 2 |
4 | 1, 3 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 class class class wbr 3976 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-un 3115 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 |
This theorem is referenced by: eqbrtrri 3999 3brtr4i 4006 exmidonfinlem 7140 neg1lt0 8956 halflt1 9065 3halfnz 9279 declei 9348 numlti 9349 faclbnd3 10645 geo2lim 11443 0.999... 11448 geoihalfsum 11449 fprodap0 11548 fprodap0f 11563 tan0 11658 cos2bnd 11687 sin4lt0 11693 eirraplem 11703 1nprm 12025 znnen 12274 tan4thpi 13309 ex-fl 13449 trilpolemisumle 13758 |
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