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Theorem resundi 4840
 Description: Distributive law for restriction over union. Theorem 31 of [Suppes] p. 65. (Contributed by NM, 30-Sep-2002.)
Assertion
Ref Expression
resundi

Proof of Theorem resundi
StepHypRef Expression
1 xpundir 4604 . . . 4
21ineq2i 3279 . . 3
3 indi 3328 . . 3
42, 3eqtri 2161 . 2
5 df-res 4559 . 2
6 df-res 4559 . . 3
7 df-res 4559 . . 3
86, 7uneq12i 3233 . 2
94, 5, 83eqtr4i 2171 1
 Colors of variables: wff set class Syntax hints:   wceq 1332  cvv 2689   cun 3074   cin 3075   cxp 4545   cres 4549 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 2691  df-un 3080  df-in 3082  df-opab 3998  df-xp 4553  df-res 4559 This theorem is referenced by:  imaundi  4959  relresfld  5076  relcoi1  5078  resasplitss  5310  fnsnsplitss  5627  fnsnsplitdc  6409  fnfi  6833  fseq1p1m1  9905  resunimafz0  10606
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