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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 3777 | . 2 |
5 | 1, 4 | mpbid 135 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 class class class wbr 3764 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 |
This theorem is referenced by: ofrval 5722 phplem2 6316 ltaddnq 6505 prarloclemarch2 6517 prmuloclemcalc 6663 axcaucvglemcau 6972 apreap 7578 ltmul1 7583 subap0d 7631 divap1d 7776 lemul2a 7825 monoord2 9236 expubnd 9311 bernneq2 9370 resqrexlemcalc2 9613 resqrexlemcalc3 9614 abs2dif2 9703 |
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