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Theorem caovcan 5665
 Description: Convert an operation cancellation law to class notation. (Contributed by NM, 20-Aug-1995.)
Hypotheses
Ref Expression
caovcan.1
caovcan.2
Assertion
Ref Expression
caovcan
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovcan
StepHypRef Expression
1 oveq1 5519 . . . 4
2 oveq1 5519 . . . 4
31, 2eqeq12d 2054 . . 3
43imbi1d 220 . 2
5 oveq2 5520 . . . 4
65eqeq1d 2048 . . 3
7 eqeq1 2046 . . 3
86, 7imbi12d 223 . 2
9 caovcan.1 . . 3
10 oveq2 5520 . . . . . 6
1110eqeq2d 2051 . . . . 5
12 eqeq2 2049 . . . . 5
1311, 12imbi12d 223 . . . 4
1413imbi2d 219 . . 3
15 caovcan.2 . . 3
169, 14, 15vtocl 2608 . 2
174, 8, 16vtocl2ga 2621 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243   wcel 1393  cvv 2557  (class class class)co 5512 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-ov 5515 This theorem is referenced by: (None)
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