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Mirrors > Home > ILE Home > Th. List > caov42d | Unicode version |
Description: Rearrange arguments in a commutative, associative operation. (Contributed by NM, 26-Aug-1995.) (Revised by Mario Carneiro, 30-Dec-2014.) |
Ref | Expression |
---|---|
caovd.1 |
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caovd.2 |
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caovd.3 |
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caovd.com |
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caovd.ass |
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caovd.4 |
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caovd.cl |
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Ref | Expression |
---|---|
caov42d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovd.1 |
. . 3
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2 | caovd.2 |
. . 3
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3 | caovd.3 |
. . 3
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4 | caovd.com |
. . 3
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5 | caovd.ass |
. . 3
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6 | caovd.4 |
. . 3
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7 | caovd.cl |
. . 3
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8 | 1, 2, 3, 4, 5, 6, 7 | caov4d 5845 |
. 2
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9 | 4, 2, 6 | caovcomd 5817 |
. . 3
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10 | 9 | oveq2d 5684 |
. 2
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11 | 8, 10 | eqtrd 2121 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2624 df-un 3006 df-sn 3458 df-pr 3459 df-op 3461 df-uni 3662 df-br 3854 df-iota 4995 df-fv 5038 df-ov 5671 |
This theorem is referenced by: caovlem2d 5853 mulcmpblnrlemg 7349 ltasrg 7379 axmulass 7471 |
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