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Theorem caovcan 5607
 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 5462 . . . 4
2 oveq1 5462 . . . 4
31, 2eqeq12d 2051 . . 3
43imbi1d 220 . 2
5 oveq2 5463 . . . 4
65eqeq1d 2045 . . 3
7 eqeq1 2043 . . 3
86, 7imbi12d 223 . 2
9 caovcan.1 . . 3
10 oveq2 5463 . . . . . 6
1110eqeq2d 2048 . . . . 5
12 eqeq2 2046 . . . . 5
1311, 12imbi12d 223 . . . 4
1413imbi2d 219 . . 3
15 caovcan.2 . . 3
169, 14, 15vtocl 2602 . 2
174, 8, 16vtocl2ga 2615 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1242   wcel 1390  cvv 2551  (class class class)co 5455 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853  df-ov 5458 This theorem is referenced by: (None)
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