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Theorem resundi 4625
 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 4397 . . . 4
21ineq2i 3135 . . 3
3 indi 3184 . . 3
42, 3eqtri 2060 . 2
5 df-res 4357 . 2
6 df-res 4357 . . 3
7 df-res 4357 . . 3
86, 7uneq12i 3095 . 2
94, 5, 83eqtr4i 2070 1
 Colors of variables: wff set class Syntax hints:   wceq 1243  cvv 2557   cun 2915   cin 2916   cxp 4343   cres 4347 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-opab 3819  df-xp 4351  df-res 4357 This theorem is referenced by:  imaundi  4736  relresfld  4847  relcoi1  4849  resasplitss  5069  fseq1p1m1  8956
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