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Theorem caov31 5715
 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
caov31
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caov31
StepHypRef Expression
1 caov.1 . . . 4
2 caov.3 . . . 4
3 caov.2 . . . 4
4 caov.ass . . . 4
51, 2, 3, 4caovass 5686 . . 3
6 caov.com . . . 4
71, 2, 3, 6, 4caov12 5714 . . 3
85, 7eqtri 2102 . 2
91, 3, 2, 6, 4caov32 5713 . 2
102, 1, 3, 6, 4caov32 5713 . . 3
112, 1, 3, 4caovass 5686 . . 3
1210, 11eqtr3i 2104 . 2
138, 9, 123eqtr4i 2112 1
 Colors of variables: wff set class Syntax hints:   wceq 1285   wcel 1434  cvv 2602  (class class class)co 5537 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-sn 3406  df-pr 3407  df-op 3409  df-uni 3604  df-br 3788  df-iota 4891  df-fv 4934  df-ov 5540 This theorem is referenced by:  caov13  5716
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