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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 | |
caovd.2 | |
caovd.3 | |
caovd.com | |
caovd.ass |
Ref | Expression |
---|---|
caov32d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovd.com | . . . 4 | |
2 | caovd.2 | . . . 4 | |
3 | caovd.3 | . . . 4 | |
4 | 1, 2, 3 | caovcomd 5998 | . . 3 |
5 | 4 | oveq2d 5858 | . 2 |
6 | caovd.ass | . . 3 | |
7 | caovd.1 | . . 3 | |
8 | 6, 7, 2, 3 | caovassd 6001 | . 2 |
9 | 6, 7, 3, 2 | caovassd 6001 | . 2 |
10 | 5, 8, 9 | 3eqtr4d 2208 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 968 wceq 1343 wcel 2136 (class class class)co 5842 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-ext 2147 |
This theorem depends on definitions: df-bi 116 df-3an 970 df-tru 1346 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-ral 2449 df-rex 2450 df-v 2728 df-un 3120 df-sn 3582 df-pr 3583 df-op 3585 df-uni 3790 df-br 3983 df-iota 5153 df-fv 5196 df-ov 5845 |
This theorem is referenced by: caov31d 6024 mulcanenq 7326 mulcanenq0ec 7386 ltexprlemrl 7551 ltexprlemru 7553 cauappcvgprlemladdfl 7596 cauappcvgprlemladdru 7597 mulcmpblnrlemg 7681 ltsosr 7705 recexgt0sr 7714 mulgt0sr 7719 caucvgsrlemoffcau 7739 caucvgsrlemoffres 7741 resqrexlemover 10952 |
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