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Theorem resiun1 5129
 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 4333 . 2
2 df-res 4851 . . . . 5
3 incom 3616 . . . . 5
42, 3eqtri 2493 . . . 4
54a1i 11 . . 3
65iuneq2i 4288 . 2
7 df-res 4851 . . 3
8 incom 3616 . . 3
97, 8eqtri 2493 . 2
101, 6, 93eqtr4ri 2504 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-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  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-ral 2761  df-rex 2762  df-v 3033  df-in 3397  df-ss 3404  df-iun 4271  df-res 4851 This theorem is referenced by: (None)
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