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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 5948 | . 2 |
9 | 4, 2, 6 | caovcomd 5920 | . . 3 |
10 | 9 | oveq2d 5783 | . 2 |
11 | 8, 10 | eqtrd 2170 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 962 wceq 1331 wcel 1480 (class class class)co 5767 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-iota 5083 df-fv 5126 df-ov 5770 |
This theorem is referenced by: caovlem2d 5956 mulcmpblnrlemg 7541 ltasrg 7571 axmulass 7674 |
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