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Theorem caovord 5946
 Description: Convert an operation ordering law to class notation. (Contributed by NM, 19-Feb-1996.)
Hypotheses
Ref Expression
caovord.1
caovord.2
caovord.3
Assertion
Ref Expression
caovord
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovord
StepHypRef Expression
1 oveq1 5785 . . . 4
2 oveq1 5785 . . . 4
31, 2breq12d 3946 . . 3
43bibi2d 231 . 2
5 caovord.1 . . 3
6 caovord.2 . . 3
7 breq1 3936 . . . . . 6
8 oveq2 5786 . . . . . . 7
98breq1d 3943 . . . . . 6
107, 9bibi12d 234 . . . . 5
11 breq2 3937 . . . . . 6
12 oveq2 5786 . . . . . . 7
1312breq2d 3945 . . . . . 6
1411, 13bibi12d 234 . . . . 5
1510, 14sylan9bb 458 . . . 4
1615imbi2d 229 . . 3
17 caovord.3 . . 3
185, 6, 16, 17vtocl2 2742 . 2
194, 18vtoclga 2753 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1332   wcel 1481  cvv 2687   class class class wbr 3933  (class class class)co 5778 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-v 2689  df-un 3076  df-sn 3534  df-pr 3535  df-op 3537  df-uni 3741  df-br 3934  df-iota 5092  df-fv 5135  df-ov 5781 This theorem is referenced by:  caovord2  5947  caovord3  5948
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