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Mirrors > Home > ILE Home > Th. List > oveq123d | Unicode version |
Description: Equality deduction for operation value. (Contributed by FL, 22-Dec-2008.) |
Ref | Expression |
---|---|
oveq123d.1 |
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oveq123d.2 |
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oveq123d.3 |
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Ref | Expression |
---|---|
oveq123d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq123d.1 |
. . 3
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2 | 1 | oveqd 5914 |
. 2
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3 | oveq123d.2 |
. . 3
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4 | oveq123d.3 |
. . 3
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5 | 3, 4 | oveq12d 5915 |
. 2
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6 | 2, 5 | eqtrd 2222 |
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-3an 982 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-v 2754 df-un 3148 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-iota 5196 df-fv 5243 df-ov 5900 |
This theorem is referenced by: csbov123g 5935 issgrp 12881 sgrp1 12889 issgrpd 12890 ismndd 12913 grpsubfvalg 13004 grpsubpropdg 13063 imasgrp 13068 subgsub 13142 releqgg 13176 eqgex 13177 eqgfval 13178 isrng 13305 isrngd 13324 issrg 13336 srgidmlem 13349 isring 13371 ringass 13387 ringidmlem 13393 isringd 13412 ring1 13428 unitlinv 13493 unitrinv 13494 dvrfvald 13500 islmodd 13626 islidlm 13812 rnglidlmsgrp 13830 rnglidlrng 13831 psrval 13961 |
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