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Mirrors > Home > ILE Home > Th. List > caov411d | 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 | |
caovd.4 | |
caovd.cl |
Ref | Expression |
---|---|
caov411d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovd.2 | . . 3 | |
2 | caovd.1 | . . 3 | |
3 | caovd.3 | . . 3 | |
4 | caovd.com | . . 3 | |
5 | caovd.ass | . . 3 | |
6 | caovd.4 | . . 3 | |
7 | caovd.cl | . . 3 | |
8 | 1, 2, 3, 4, 5, 6, 7 | caov4d 5923 | . 2 |
9 | 4, 1, 2 | caovcomd 5895 | . . 3 |
10 | 9 | oveq1d 5757 | . 2 |
11 | 4, 1, 3 | caovcomd 5895 | . . 3 |
12 | 11 | oveq1d 5757 | . 2 |
13 | 8, 10, 12 | 3eqtr3d 2158 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 947 wceq 1316 wcel 1465 (class class class)co 5742 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 |
This theorem is referenced by: ecopovtrn 6494 ecopovtrng 6497 ltsonq 7174 ltanqg 7176 mulextsr1lem 7556 |
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