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Mirrors > Home > ILE Home > Th. List > caov13d | 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 |
---|---|
caov13d |
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 | 1, 2, 3, 4, 5 | caov31d 6015 | . 2 |
7 | 5, 1, 2, 3 | caovassd 5992 | . 2 |
8 | 5, 3, 2, 1 | caovassd 5992 | . 2 |
9 | 6, 7, 8 | 3eqtr3d 2205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 967 wceq 1342 wcel 2135 (class class class)co 5836 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-iota 5147 df-fv 5190 df-ov 5839 |
This theorem is referenced by: enq0tr 7366 mullocprlem 7502 mulcmpblnrlemg 7672 |
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