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Mirrors > Home > MPE Home > Th. List > caovclg | Structured version Unicode version |
Description: Convert an operation closure law to class notation. (Contributed by Mario Carneiro, 26-May-2014.) |
Ref | Expression |
---|---|
caovclg.1 |
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Ref | Expression |
---|---|
caovclg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovclg.1 |
. . 3
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2 | 1 | ralrimivva 2908 |
. 2
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3 | oveq1 6202 |
. . . 4
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4 | 3 | eleq1d 2521 |
. . 3
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5 | oveq2 6203 |
. . . 4
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6 | 5 | eleq1d 2521 |
. . 3
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7 | 4, 6 | rspc2v 3180 |
. 2
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8 | 2, 7 | mpan9 469 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1954 ax-ext 2431 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2602 df-ral 2801 df-rex 2802 df-rab 2805 df-v 3074 df-dif 3434 df-un 3436 df-in 3438 df-ss 3445 df-nul 3741 df-if 3895 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4195 df-br 4396 df-iota 5484 df-fv 5529 df-ov 6198 |
This theorem is referenced by: caovcld 6361 caovcl 6362 grprinvd 6407 seqcl2 11936 seqcaopr 11955 ercpbl 14601 imasmnd2 15572 gsumpropd2lem 15619 imasgrp2 15784 gsumzaddlem 16524 gsumzaddlemOLD 16526 imasrng 16829 divsrhm 17437 mplind 17703 plymullem 21812 |
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