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Theorem caov411 6279
 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
caov.4
Assertion
Ref Expression
caov411
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caov411
StepHypRef Expression
1 caov.1 . . . 4
2 caov.2 . . . 4
3 caov.3 . . . 4
4 caov.com . . . 4
5 caov.ass . . . 4
61, 2, 3, 4, 5caov31 6276 . . 3
76oveq1i 6091 . 2
8 ovex 6106 . . 3
9 caov.4 . . 3
108, 3, 9, 5caovass 6247 . 2
11 ovex 6106 . . 3
1211, 1, 9, 5caovass 6247 . 2
137, 10, 123eqtr3i 2464 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725  cvv 2956  (class class class)co 6081 This theorem is referenced by:  ecopovtrn  7007  distrnq  8838  lterpq  8847  ltanq  8848  prlem936  8924 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-nul 4338 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-ov 6084
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