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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 5885 |
. 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 5886 |
. 2
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6 | 2, 5 | eqtrd 2210 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2739 df-un 3133 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-iota 5173 df-fv 5219 df-ov 5871 |
This theorem is referenced by: csbov123g 5906 issgrp 12688 sgrp1 12695 ismndd 12717 grpsubfvalg 12795 grpsubpropdg 12850 issrg 12961 srgidmlem 12974 isring 12996 ringass 13012 ringidmlem 13018 isringd 13033 ring1 13049 unitlinv 13107 unitrinv 13108 |
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