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Theorem resiun2 5298
Description: Distribution of restriction over indexed union. (Contributed by Mario Carneiro, 29-May-2015.)
Assertion
Ref Expression
resiun2
Distinct variable group:   ,

Proof of Theorem resiun2
StepHypRef Expression
1 df-res 5016 . 2
2 df-res 5016 . . . . 5
32a1i 11 . . . 4
43iuneq2i 4349 . . 3
5 xpiundir 5060 . . . . 5
65ineq2i 3696 . . . 4
7 iunin2 4394 . . . 4
86, 7eqtr4i 2489 . . 3
94, 8eqtr4i 2489 . 2
101, 9eqtr4i 2489 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  e.wcel 1818   cvv 3109  i^icin 3474  U_ciun 4330  X.cxp 5002  |`cres 5006
This theorem is referenced by:  fvn0ssdmfun  6022  dprd2da  17091
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-iun 4332  df-opab 4511  df-xp 5010  df-res 5016
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