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Theorem caovcanrd 5974
 Description: Commute the arguments of an operation cancellation law. (Contributed by Mario Carneiro, 30-Dec-2014.)
Hypotheses
Ref Expression
caovcang.1
caovcand.2
caovcand.3
caovcand.4
caovcanrd.5
caovcanrd.6
Assertion
Ref Expression
caovcanrd
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovcanrd
StepHypRef Expression
1 caovcanrd.6 . . . 4
2 caovcanrd.5 . . . 4
3 caovcand.3 . . . 4
41, 2, 3caovcomd 5967 . . 3
5 caovcand.4 . . . 4
61, 2, 5caovcomd 5967 . . 3
74, 6eqeq12d 2169 . 2
8 caovcang.1 . . 3
9 caovcand.2 . . 3
108, 9, 3, 5caovcand 5973 . 2
117, 10bitr3d 189 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   w3a 963   wceq 1332   wcel 2125  (class class class)co 5814 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-rex 2438  df-v 2711  df-un 3102  df-sn 3562  df-pr 3563  df-op 3565  df-uni 3769  df-br 3962  df-iota 5128  df-fv 5171  df-ov 5817 This theorem is referenced by: (None)
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