Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  caov13 Unicode version

Theorem caov13 5961
 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
caov13
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caov13
StepHypRef Expression
1 caov.1 . . 3
2 caov.2 . . 3
3 caov.3 . . 3
4 caov.com . . 3
5 caov.ass . . 3
61, 2, 3, 4, 5caov31 5960 . 2
71, 2, 3, 5caovass 5931 . 2
83, 2, 1, 5caovass 5931 . 2
96, 7, 83eqtr3i 2168 1
 Colors of variables: wff set class Syntax hints:   wceq 1331   wcel 1480  cvv 2686  (class class class)co 5774 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-iota 5088  df-fv 5131  df-ov 5777 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator