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Theorem caov411d 5686
 Description: Rearrange arguments in a commutative, associative operation. (Contributed by NM, 26-Aug-1995.) (Revised by Mario Carneiro, 30-Dec-2014.)
Hypotheses
Ref Expression
caovd.1
caovd.2
caovd.3
caovd.com
caovd.ass
caovd.4
caovd.cl
Assertion
Ref Expression
caov411d
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caov411d
StepHypRef Expression
1 caovd.2 . . 3
2 caovd.1 . . 3
3 caovd.3 . . 3
4 caovd.com . . 3
5 caovd.ass . . 3
6 caovd.4 . . 3
7 caovd.cl . . 3
81, 2, 3, 4, 5, 6, 7caov4d 5685 . 2
94, 1, 2caovcomd 5657 . . 3
109oveq1d 5527 . 2
114, 1, 3caovcomd 5657 . . 3
1211oveq1d 5527 . 2
138, 10, 123eqtr3d 2080 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:  ecopovtrn  6203  ecopovtrng  6206  ltsonq  6496  ltanqg  6498  mulextsr1lem  6864
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