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Theorem caovcan 6253
 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 6090 . . . 4
2 oveq1 6090 . . . 4
31, 2eqeq12d 2452 . . 3
43imbi1d 310 . 2
5 oveq2 6091 . . . 4
65eqeq1d 2446 . . 3
7 eqeq1 2444 . . 3
86, 7imbi12d 313 . 2
9 caovcan.1 . . 3
10 oveq2 6091 . . . . . 6
1110eqeq2d 2449 . . . . 5
12 eqeq2 2447 . . . . 5
1311, 12imbi12d 313 . . . 4
1413imbi2d 309 . . 3
15 caovcan.2 . . 3
169, 14, 15vtocl 3008 . 2
174, 8, 16vtocl2ga 3021 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  cvv 2958  (class class class)co 6083 This theorem is referenced by:  ecopovtrn  7009 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464  df-ov 6086
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