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Theorem caovdi 5950
 Description: Convert an operation distributive law to class notation. (Contributed by NM, 25-Aug-1995.) (Revised by Mario Carneiro, 28-Jun-2013.)
Hypotheses
Ref Expression
caovdi.1
caovdi.2
caovdi.3
caovdi.4
Assertion
Ref Expression
caovdi
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovdi
StepHypRef Expression
1 caovdi.1 . 2
2 caovdi.2 . 2
3 caovdi.3 . 2
4 tru 1335 . . 3
5 caovdi.4 . . . . 5
65a1i 9 . . . 4
76caovdig 5945 . . 3
84, 7mpan 420 . 2
91, 2, 3, 8mp3an 1315 1
 Colors of variables: wff set class Syntax hints:   wa 103   w3a 962   wceq 1331   wtru 1332   wcel 1480  cvv 2686  (class class class)co 5774 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 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-iota 5088  df-fv 5131  df-ov 5777 This theorem is referenced by: (None)
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