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Theorem indir 3331
 Description: Distributive law for intersection over union. Theorem 28 of [Suppes] p. 27. (Contributed by NM, 30-Sep-2002.)
Assertion
Ref Expression
indir

Proof of Theorem indir
StepHypRef Expression
1 indi 3329 . 2
2 incom 3274 . 2
3 incom 3274 . . 3
4 incom 3274 . . 3
53, 4uneq12i 3234 . 2
61, 2, 53eqtr4i 2171 1
 Colors of variables: wff set class Syntax hints:   wceq 1332   cun 3075   cin 3076 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 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-un 3081  df-in 3083 This theorem is referenced by:  difundir  3335  undisj1  3426  disjpr2  3596  resundir  4843  djuassen  7096
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