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Mirrors > Home > ILE Home > Th. List > breqtrri | Unicode version |
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
breqtrr.1 | |
breqtrr.2 |
Ref | Expression |
---|---|
breqtrri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breqtrr.1 | . 2 | |
2 | breqtrr.2 | . . 3 | |
3 | 2 | eqcomi 2168 | . 2 |
4 | 1, 3 | breqtri 4001 | 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: 3brtr4i 4006 ensn1 6753 pw1dom2 7174 0lt1sr 7697 0le2 8938 2pos 8939 3pos 8942 4pos 8945 5pos 8948 6pos 8949 7pos 8950 8pos 8951 9pos 8952 1lt2 9017 2lt3 9018 3lt4 9020 4lt5 9023 5lt6 9027 6lt7 9032 7lt8 9038 8lt9 9045 nn0le2xi 9155 numltc 9338 declti 9350 sqge0i 10531 faclbnd2 10644 ege2le3 11598 cos2bnd 11687 3dvdsdec 11787 n2dvdsm1 11835 n2dvds3 11837 pockthi 12267 dveflem 13234 tangtx 13306 ex-fl 13449 |
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