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Mirrors > Home > ILE Home > Th. List > caov31 | Unicode version |
Description: Rearrange arguments in a commutative, associative operation. (Contributed by NM, 26-Aug-1995.) |
Ref | Expression |
---|---|
caov.1 | |
caov.2 | |
caov.3 | |
caov.com | |
caov.ass |
Ref | Expression |
---|---|
caov31 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caov.1 | . . . 4 | |
2 | caov.3 | . . . 4 | |
3 | caov.2 | . . . 4 | |
4 | caov.ass | . . . 4 | |
5 | 1, 2, 3, 4 | caovass 5996 | . . 3 |
6 | caov.com | . . . 4 | |
7 | 1, 2, 3, 6, 4 | caov12 6024 | . . 3 |
8 | 5, 7 | eqtri 2185 | . 2 |
9 | 1, 3, 2, 6, 4 | caov32 6023 | . 2 |
10 | 2, 1, 3, 6, 4 | caov32 6023 | . . 3 |
11 | 2, 1, 3, 4 | caovass 5996 | . . 3 |
12 | 10, 11 | eqtr3i 2187 | . 2 |
13 | 8, 9, 12 | 3eqtr4i 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wcel 2135 cvv 2724 (class class class)co 5839 |
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 2726 df-un 3118 df-sn 3579 df-pr 3580 df-op 3582 df-uni 3787 df-br 3980 df-iota 5150 df-fv 5193 df-ov 5842 |
This theorem is referenced by: caov13 6026 |
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