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Theorem caovcan 6478
 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 6303 . . . 4
2 oveq1 6303 . . . 4
31, 2eqeq12d 2479 . . 3
43imbi1d 317 . 2
5 oveq2 6304 . . . 4
65eqeq1d 2459 . . 3
7 eqeq1 2461 . . 3
86, 7imbi12d 320 . 2
9 caovcan.1 . . 3
10 oveq2 6304 . . . . . 6
1110eqeq2d 2471 . . . . 5
12 eqeq2 2472 . . . . 5
1311, 12imbi12d 320 . . . 4
1413imbi2d 316 . . 3
15 caovcan.2 . . 3
169, 14, 15vtocl 3161 . 2
174, 8, 16vtocl2ga 3175 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1395   wcel 1819  cvv 3109  (class class class)co 6296 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-br 4457  df-iota 5557  df-fv 5602  df-ov 6299 This theorem is referenced by:  ecopovtrn  7432
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