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Mirrors > Home > ILE Home > Th. List > caovassg | Unicode version |
Description: Convert an operation associative law to class notation. (Contributed by Mario Carneiro, 1-Jun-2013.) (Revised by Mario Carneiro, 26-May-2014.) |
Ref | Expression |
---|---|
caovassg.1 |
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Ref | Expression |
---|---|
caovassg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovassg.1 |
. . 3
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2 | 1 | ralrimivvva 2573 |
. 2
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3 | oveq1 5903 |
. . . . 5
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4 | 3 | oveq1d 5911 |
. . . 4
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5 | oveq1 5903 |
. . . 4
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6 | 4, 5 | eqeq12d 2204 |
. . 3
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7 | oveq2 5904 |
. . . . 5
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8 | 7 | oveq1d 5911 |
. . . 4
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9 | oveq1 5903 |
. . . . 5
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10 | 9 | oveq2d 5912 |
. . . 4
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11 | 8, 10 | eqeq12d 2204 |
. . 3
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12 | oveq2 5904 |
. . . 4
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13 | oveq2 5904 |
. . . . 5
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14 | 13 | oveq2d 5912 |
. . . 4
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15 | 12, 14 | eqeq12d 2204 |
. . 3
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16 | 6, 11, 15 | rspc3v 2872 |
. 2
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17 | 2, 16 | mpan9 281 |
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-ral 2473 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 5899 |
This theorem is referenced by: caovassd 6056 caovass 6057 seq3split 10510 seq3caopr 10514 grpinvalem 12861 grpinva 12862 grprida 12863 |
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