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Mirrors > Home > ILE Home > Th. List > caov12d | 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 |
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caovd.2 |
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caovd.3 |
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caovd.com |
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caovd.ass |
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Ref | Expression |
---|---|
caov12d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovd.com |
. . . 4
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2 | caovd.1 |
. . . 4
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3 | caovd.2 |
. . . 4
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4 | 1, 2, 3 | caovcomd 6053 |
. . 3
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5 | 4 | oveq1d 5911 |
. 2
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6 | caovd.ass |
. . 3
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7 | caovd.3 |
. . 3
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8 | 6, 2, 3, 7 | caovassd 6056 |
. 2
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9 | 6, 3, 2, 7 | caovassd 6056 |
. 2
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10 | 5, 8, 9 | 3eqtr3d 2230 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-iota 5196 df-fv 5243 df-ov 5899 |
This theorem is referenced by: caov4d 6081 caovimo 6090 ltaddnq 7436 ltexnqq 7437 enq0tr 7463 mullocprlem 7599 1idprl 7619 1idpru 7620 cauappcvgprlemdisj 7680 mulcmpblnrlemg 7769 lttrsr 7791 ltsosr 7793 0idsr 7796 1idsr 7797 recexgt0sr 7802 mulgt0sr 7807 axmulass 7902 |
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