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Mirrors > Home > ILE Home > Th. List > oveqd | Unicode version |
Description: Equality deduction for operation value. (Contributed by NM, 9-Sep-2006.) |
Ref | Expression |
---|---|
oveq1d.1 |
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Ref | Expression |
---|---|
oveqd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1d.1 |
. 2
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2 | oveq 5903 |
. 2
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3 | 1, 2 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rex 2474 df-uni 3825 df-br 4019 df-iota 5196 df-fv 5243 df-ov 5900 |
This theorem is referenced by: oveq123d 5918 oveqdr 5925 csbov12g 5936 ovmpodxf 6023 oprssov 6039 ofeqd 6109 ofeq 6110 fnmpoovd 6241 seqeq2 10482 prdsex 12777 imasex 12785 imasival 12786 plusffvalg 12841 mgm1 12849 grpidvalg 12852 grpidd 12862 gsumress 12873 sgrp1 12889 issgrpd 12890 ismndd 12913 issubmnd 12918 mnd1 12922 ismhm 12928 mhmex 12929 issubm 12939 resmhm 12954 resmhm2 12955 resmhm2b 12956 isgrp 12966 isgrpd2e 12980 grpidd2 13000 grpinvfvalg 13001 grp1 13065 imasgrp2 13067 imasgrp 13068 subg0 13136 subginv 13137 subgcl 13140 issubgrpd2 13146 isnsg 13158 nmznsg 13169 isghm 13199 resghm 13216 iscmn 13249 iscmnd 13254 imasabl 13290 rngass 13310 rngcl 13315 rngpropd 13326 dfur2g 13333 issrg 13336 srgcl 13341 srgass 13342 srgideu 13343 issrgid 13352 srgpcomp 13361 srgpcompp 13362 isring 13371 ringcl 13384 crngcom 13385 iscrng2 13386 ringass 13387 ringideu 13388 isringid 13396 ringidss 13400 ringpropd 13409 ring1 13428 opprmulg 13438 oppr0g 13448 oppr1g 13449 opprnegg 13450 mulgass3 13452 reldvdsrsrg 13459 dvdsrvald 13460 dvdsrd 13461 opprunitd 13477 dvrvald 13501 rdivmuldivd 13511 rhmmul 13531 isrhm2d 13532 rhmopp 13543 rhmunitinv 13545 islring 13556 lringuplu 13560 subrngmcl 13573 subrg1 13595 subrgmcl 13597 subrgdvds 13599 subrguss 13600 subrginv 13601 subrgdv 13602 subrgunit 13603 subrgugrp 13604 issubrg3 13611 aprval 13615 aprap 13619 islmod 13624 islmodd 13626 scaffvalg 13639 lmodpropd 13682 lsssetm 13689 islssmd 13692 islidlm 13812 lidlacl 13817 rnglidlmmgm 13829 rnglidlmsgrp 13830 rnglidlrng 13831 psrval 13961 psradd 13972 blfvalps 14362 |
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