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

Theorem caovordig 5943
 Description: Convert an operation ordering law to class notation. (Contributed by Mario Carneiro, 31-Dec-2014.)
Hypothesis
Ref Expression
caovordig.1
Assertion
Ref Expression
caovordig
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovordig
StepHypRef Expression
1 caovordig.1 . . 3
21ralrimivvva 2518 . 2
3 breq1 3939 . . . 4
4 oveq2 5789 . . . . 5
54breq1d 3946 . . . 4
63, 5imbi12d 233 . . 3
7 breq2 3940 . . . 4
8 oveq2 5789 . . . . 5
98breq2d 3948 . . . 4
107, 9imbi12d 233 . . 3
11 oveq1 5788 . . . . 5
12 oveq1 5788 . . . . 5
1311, 12breq12d 3949 . . . 4
1413imbi2d 229 . . 3
156, 10, 14rspc3v 2808 . 2
162, 15mpan9 279 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   w3a 963   wceq 1332   wcel 1481  wral 2417   class class class wbr 3936  (class class class)co 5781 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-ral 2422  df-rex 2423  df-v 2691  df-un 3079  df-sn 3537  df-pr 3538  df-op 3540  df-uni 3744  df-br 3937  df-iota 5095  df-fv 5138  df-ov 5784 This theorem is referenced by:  caovordid  5944
 Copyright terms: Public domain W3C validator