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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 | |
caovd.2 | |
caovd.3 | |
caovd.com | |
caovd.ass | |
caovd.4 | |
caovd.cl |
Ref | Expression |
---|---|
caov42d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovd.1 | . . 3 | |
2 | caovd.2 | . . 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 5685 | . 2 |
9 | 4, 2, 6 | caovcomd 5657 | . . 3 |
10 | 9 | oveq2d 5528 | . 2 |
11 | 8, 10 | eqtrd 2072 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 w3a 885 wceq 1243 wcel 1393 (class class class)co 5512 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-iota 4867 df-fv 4910 df-ov 5515 |
This theorem is referenced by: caovlem2d 5693 mulcmpblnrlemg 6825 ltasrg 6855 axmulass 6947 |
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