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Mirrors > Home > ILE Home > Th. List > caov32d | 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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Ref | Expression |
---|---|
caov32d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovd.com |
. . . 4
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2 | caovd.2 |
. . . 4
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3 | caovd.3 |
. . . 4
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4 | 1, 2, 3 | caovcomd 5801 |
. . 3
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5 | 4 | oveq2d 5668 |
. 2
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6 | caovd.ass |
. . 3
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7 | caovd.1 |
. . 3
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8 | 6, 7, 2, 3 | caovassd 5804 |
. 2
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9 | 6, 7, 3, 2 | caovassd 5804 |
. 2
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10 | 5, 8, 9 | 3eqtr4d 2130 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-v 2621 df-un 3003 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-br 3846 df-iota 4980 df-fv 5023 df-ov 5655 |
This theorem is referenced by: caov31d 5827 mulcanenq 6942 mulcanenq0ec 7002 ltexprlemrl 7167 ltexprlemru 7169 cauappcvgprlemladdfl 7212 cauappcvgprlemladdru 7213 mulcmpblnrlemg 7284 ltsosr 7308 recexgt0sr 7317 mulgt0sr 7321 caucvgsrlemoffcau 7341 caucvgsrlemoffres 7343 resqrexlemover 10439 |
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