Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  caov13d Structured version   Unicode version

Theorem caov13d 6262
 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
Assertion
Ref Expression
caov13d
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caov13d
StepHypRef Expression
1 caovd.1 . . 3
2 caovd.2 . . 3
3 caovd.3 . . 3
4 caovd.com . . 3
5 caovd.ass . . 3
61, 2, 3, 4, 5caov31d 6261 . 2
75, 1, 2, 3caovassd 6238 . 2
85, 3, 2, 1caovassd 6238 . 2
96, 7, 83eqtr3d 2475 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   w3a 936   wceq 1652   wcel 1725  (class class class)co 6073 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 2416 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-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076
 Copyright terms: Public domain W3C validator