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Theorem caov32 6275
 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
caov32
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caov32
StepHypRef Expression
1 caov.2 . . . 4
2 caov.3 . . . 4
3 caov.com . . . 4
41, 2, 3caovcom 6245 . . 3
54oveq2i 6093 . 2
6 caov.1 . . 3
7 caov.ass . . 3
86, 1, 2, 7caovass 6248 . 2
96, 2, 1, 7caovass 6248 . 2
105, 8, 93eqtr4i 2467 1
 Colors of variables: wff set class Syntax hints:   wceq 1653   wcel 1726  cvv 2957  (class class class)co 6082 This theorem is referenced by:  caov31  6277  addassnq  8836  ltexprlem7  8920  mulcmpblnrlem  8949  recexsrlem  8979  mulgt0sr  8981 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 2418 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 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-br 4214  df-iota 5419  df-fv 5463  df-ov 6085
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