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Mirrors > Home > ILE Home > Th. List > breqtri | Unicode version |
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
breqtr.1 | |
breqtr.2 |
Ref | Expression |
---|---|
breqtri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breqtr.1 | . 2 | |
2 | breqtr.2 | . . 3 | |
3 | 2 | breq2i 3984 | . 2 |
4 | 1, 3 | mpbi 144 | 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: breqtrri 4003 3brtr3i 4005 le9lt10 9339 9lt10 9443 sqrt2gt1lt2 10977 trireciplem 11427 cos1bnd 11686 cos2bnd 11687 cos01gt0 11689 sin4lt0 11693 z4even 11838 coseq00topi 13297 sincos4thpi 13302 ex-fl 13443 |
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