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Theorem caovcang 6457
 Description: Convert an operation cancellation law to class notation. (Contributed by NM, 20-Aug-1995.) (Revised by Mario Carneiro, 30-Dec-2014.)
Hypothesis
Ref Expression
caovcang.1
Assertion
Ref Expression
caovcang
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovcang
StepHypRef Expression
1 caovcang.1 . . 3
21ralrimivvva 2863 . 2
3 oveq1 6284 . . . . 5
4 oveq1 6284 . . . . 5
53, 4eqeq12d 2463 . . . 4
65bibi1d 319 . . 3
7 oveq2 6285 . . . . 5
87eqeq1d 2443 . . . 4
9 eqeq1 2445 . . . 4
108, 9bibi12d 321 . . 3
11 oveq2 6285 . . . . 5
1211eqeq2d 2455 . . . 4
13 eqeq2 2456 . . . 4
1412, 13bibi12d 321 . . 3
156, 10, 14rspc3v 3206 . 2
162, 15mpan9 469 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 972   wceq 1381   wcel 1802  wral 2791  (class class class)co 6277 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 974  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-ral 2796  df-rex 2797  df-rab 2800  df-v 3095  df-dif 3461  df-un 3463  df-in 3465  df-ss 3472  df-nul 3768  df-if 3923  df-sn 4011  df-pr 4013  df-op 4017  df-uni 4231  df-br 4434  df-iota 5537  df-fv 5582  df-ov 6280 This theorem is referenced by:  caovcand  6458  caofcan  31197
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