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Theorem resiun2 5130
 Description: Distribution of restriction over indexed union. (Contributed by Mario Carneiro, 29-May-2015.)
Assertion
Ref Expression
resiun2
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem resiun2
StepHypRef Expression
1 df-res 4851 . 2
2 df-res 4851 . . . . 5
32a1i 11 . . . 4
43iuneq2i 4288 . . 3
5 xpiundir 4895 . . . . 5
65ineq2i 3622 . . . 4
7 iunin2 4333 . . . 4
86, 7eqtr4i 2496 . . 3
94, 8eqtr4i 2496 . 2
101, 9eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1452   wcel 1904  cvv 3031   cin 3389  ciun 4269   cxp 4837   cres 4841 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-iun 4271  df-opab 4455  df-xp 4845  df-res 4851 This theorem is referenced by:  fvn0ssdmfun  6028  dprd2da  17753
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