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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 |
---|---|
3brtr4d.1 | |
3brtr4d.2 | |
3brtr4d.3 |
Ref | Expression |
---|---|
3brtr4d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3brtr4d.1 | . 2 | |
2 | 3brtr4d.2 | . . 3 | |
3 | 3brtr4d.3 | . . 3 | |
4 | 2, 3 | breq12d 3937 | . 2 |
5 | 1, 4 | mpbird 166 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 class class class wbr 3924 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 |
This theorem is referenced by: f1oiso2 5721 prarloclemarch2 7220 caucvgprprlemmu 7496 caucvgsrlembound 7595 mulap0 8408 lediv12a 8645 recp1lt1 8650 xleadd1a 9649 fldiv4p1lem1div2 10071 intfracq 10086 modqmulnn 10108 addmodlteq 10164 frecfzennn 10192 monoord2 10243 expgt1 10324 leexp2r 10340 leexp1a 10341 bernneq 10405 faclbnd 10480 faclbnd6 10483 facubnd 10484 hashunlem 10543 zfz1isolemiso 10575 sqrtgt0 10799 absrele 10848 absimle 10849 abstri 10869 abs2difabs 10873 bdtrilem 11003 bdtri 11004 xrmaxifle 11008 xrmaxadd 11023 xrbdtri 11038 climsqz 11097 climsqz2 11098 fsum3cvg2 11156 isumle 11257 expcnvap0 11264 expcnvre 11265 explecnv 11267 cvgratz 11294 efcllemp 11353 ege2le3 11366 eflegeo 11397 cos12dec 11463 phibnd 11882 psmetres2 12491 xmetres2 12537 comet 12657 bdxmet 12659 cnmet 12688 ivthdec 12780 limcimolemlt 12791 tangtx 12908 cvgcmp2nlemabs 13216 trilpolemlt1 13223 |
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