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Theorem caov12 5689
 Description: Rearrange arguments in a commutative, associative operation. (Contributed by NM, 26-Aug-1995.)
Hypotheses
Ref Expression
caov.1
caov.2
caov.3
caov.com
caov.ass
Assertion
Ref Expression
caov12
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caov12
StepHypRef Expression
1 caov.1 . . . 4
2 caov.2 . . . 4
3 caov.com . . . 4
41, 2, 3caovcom 5658 . . 3
54oveq1i 5522 . 2
6 caov.3 . . 3
7 caov.ass . . 3
81, 2, 6, 7caovass 5661 . 2
92, 1, 6, 7caovass 5661 . 2
105, 8, 93eqtr3i 2068 1
 Colors of variables: wff set class Syntax hints:   wceq 1243   wcel 1393  cvv 2557  (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:  caov31  5690
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