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Theorem caov4d 6286
 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
caov4d
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caov4d
StepHypRef Expression
1 caovd.2 . . . 4
2 caovd.3 . . . 4
3 caovd.4 . . . 4
4 caovd.com . . . 4
5 caovd.ass . . . 4
61, 2, 3, 4, 5caov12d 6283 . . 3
76oveq2d 6106 . 2
8 caovd.1 . . 3
9 caovd.cl . . . 4
109, 2, 3caovcld 6255 . . 3
115, 8, 1, 10caovassd 6261 . 2
129, 1, 3caovcld 6255 . . 3
135, 8, 2, 12caovassd 6261 . 2
147, 11, 133eqtr4d 2483 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   w3a 960   wceq 1364   wcel 1761  (class class class)co 6090 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1713  ax-7 1733  ax-10 1780  ax-11 1785  ax-12 1797  ax-13 1948  ax-ext 2422 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 962  df-tru 1367  df-ex 1592  df-nf 1595  df-sb 1706  df-clab 2428  df-cleq 2434  df-clel 2437  df-nfc 2566  df-ral 2718  df-rex 2719  df-rab 2722  df-v 2972  df-dif 3328  df-un 3330  df-in 3332  df-ss 3339  df-nul 3635  df-if 3789  df-sn 3875  df-pr 3877  df-op 3881  df-uni 4089  df-br 4290  df-iota 5378  df-fv 5423  df-ov 6093 This theorem is referenced by:  caov411d  6287  caov42d  6288
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