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Theorem resiun2 5168
 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 4892 . 2
2 df-res 4892 . . . . 5
32a1i 11 . . . 4
43iuneq2i 4113 . . 3
5 xpiundir 4935 . . . . 5
65ineq2i 3541 . . . 4
7 iunin2 4157 . . . 4
86, 7eqtr4i 2461 . . 3
94, 8eqtr4i 2461 . 2
101, 9eqtr4i 2461 1
 Colors of variables: wff set class Syntax hints:   wceq 1653   wcel 1726  cvv 2958   cin 3321  ciun 4095   cxp 4878   cres 4882 This theorem is referenced by:  dprd2da  15602 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-iun 4097  df-opab 4269  df-xp 4886  df-res 4892
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