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Theorem caov411d 6275
 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 6274 . 2
94, 1, 2caovcomd 6246 . . 3
109oveq1d 6099 . 2
114, 1, 3caovcomd 6246 . . 3
1211oveq1d 6099 . 2
138, 10, 123eqtr3d 2478 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937   wceq 1653   wcel 1726  (class class class)co 6084 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-iota 5421  df-fv 5465  df-ov 6087
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