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Theorem resiun1 4764
 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 3815 . 2
2 df-res 4479 . . . . 5
3 incom 3207 . . . . 5
42, 3eqtri 2115 . . . 4
54a1i 9 . . 3
65iuneq2i 3770 . 2
7 df-res 4479 . . 3
8 incom 3207 . . 3
97, 8eqtri 2115 . 2
101, 6, 93eqtr4ri 2126 1
 Colors of variables: wff set class Syntax hints:   wceq 1296   wcel 1445  cvv 2633   cin 3012  ciun 3752   cxp 4465   cres 4469 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-ral 2375  df-rex 2376  df-v 2635  df-in 3019  df-ss 3026  df-iun 3754  df-res 4479 This theorem is referenced by: (None)
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