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Theorem caovcang 5925
 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 2513 . 2
3 oveq1 5774 . . . . 5
4 oveq1 5774 . . . . 5
53, 4eqeq12d 2152 . . . 4
65bibi1d 232 . . 3
7 oveq2 5775 . . . . 5
87eqeq1d 2146 . . . 4
9 eqeq1 2144 . . . 4
108, 9bibi12d 234 . . 3
11 oveq2 5775 . . . . 5
1211eqeq2d 2149 . . . 4
13 eqeq2 2147 . . . 4
1412, 13bibi12d 234 . . 3
156, 10, 14rspc3v 2800 . 2
162, 15mpan9 279 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   w3a 962   wceq 1331   wcel 1480  wral 2414  (class class class)co 5767 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-rex 2420  df-v 2683  df-un 3070  df-sn 3528  df-pr 3529  df-op 3531  df-uni 3732  df-br 3925  df-iota 5083  df-fv 5126  df-ov 5770 This theorem is referenced by:  caovcand  5926
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