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Mirrors > Home > ILE Home > Th. List > 3brtr4d | Unicode version |
Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 21-Feb-2005.) |
Ref | Expression |
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3brtr4d.1 |
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3brtr4d.2 |
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3brtr4d.3 |
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Ref | Expression |
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3brtr4d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3brtr4d.1 |
. 2
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2 | 3brtr4d.2 |
. . 3
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3 | 3brtr4d.3 |
. . 3
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4 | 2, 3 | breq12d 3858 |
. 2
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5 | 1, 4 | mpbird 165 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
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 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-v 2621 df-un 3003 df-sn 3452 df-pr 3453 df-op 3455 df-br 3846 |
This theorem is referenced by: f1oiso2 5606 prarloclemarch2 6976 caucvgprprlemmu 7252 caucvgsrlembound 7337 mulap0 8121 lediv12a 8353 recp1lt1 8358 fldiv4p1lem1div2 9708 intfracq 9723 modqmulnn 9745 addmodlteq 9801 frecfzennn 9829 monoord2 9901 expgt1 9989 leexp2r 10005 leexp1a 10006 bernneq 10070 faclbnd 10145 faclbnd6 10148 facubnd 10149 hashunlem 10208 zfz1isolemiso 10240 sqrtgt0 10463 absrele 10512 absimle 10513 abstri 10533 abs2difabs 10537 climsqz 10719 climsqz2 10720 fisumcvg2 10782 fsum3cvg2 10783 isumle 10885 expcnvap0 10892 expcnvre 10893 explecnv 10895 cvgratz 10922 efcllemp 10944 ege2le3 10957 eflegeo 10988 phibnd 11467 |
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