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Theorem resiun1 5165
 Description: Distribution of restriction over indexed union. (Contributed by Mario Carneiro, 29-May-2015.)
Assertion
Ref Expression
resiun1
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem resiun1
StepHypRef Expression
1 iunin2 4155 . 2
2 df-res 4890 . . . . 5
3 incom 3533 . . . . 5
42, 3eqtri 2456 . . . 4
54a1i 11 . . 3
65iuneq2i 4111 . 2
7 df-res 4890 . . 3
8 incom 3533 . . 3
97, 8eqtri 2456 . 2
101, 6, 93eqtr4ri 2467 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725  cvv 2956   cin 3319  ciun 4093   cxp 4876   cres 4880 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-v 2958  df-in 3327  df-ss 3334  df-iun 4095  df-res 4890
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