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Mirrors > Home > ILE Home > Th. List > 3brtr3d | Unicode version |
Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 18-Oct-1999.) |
Ref | Expression |
---|---|
3brtr3d.1 | |
3brtr3d.2 | |
3brtr3d.3 |
Ref | Expression |
---|---|
3brtr3d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3brtr3d.1 | . 2 | |
2 | 3brtr3d.2 | . . 3 | |
3 | 3brtr3d.3 | . . 3 | |
4 | 2, 3 | breq12d 3798 | . 2 |
5 | 1, 4 | mpbid 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 class class class wbr 3785 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-un 2977 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 |
This theorem is referenced by: ofrval 5742 phplem2 6339 ltaddnq 6597 prarloclemarch2 6609 prmuloclemcalc 6755 axcaucvglemcau 7064 apreap 7687 ltmul1 7692 subap0d 7740 divap1d 7888 lemul2a 7937 monoord2 9456 expubnd 9533 bernneq2 9594 resqrexlemcalc2 9901 resqrexlemcalc3 9902 abs2dif2 9993 |
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