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Theorem iinuni 3883
 Description: A relationship involving union and indexed intersection. Exercise 23 of [Enderton] p. 33. (Contributed by NM, 25-Nov-2003.) (Proof shortened by Mario Carneiro, 17-Nov-2016.)
Assertion
Ref Expression
iinuni
Distinct variable groups:   ,   ,

Proof of Theorem iinuni
StepHypRef Expression
1 r19.32v 2648 . . . 4
2 elun 3226 . . . . 5
32ralbii 2531 . . . 4
4 vex 2730 . . . . . 6
54elint2 3767 . . . . 5
65orbi2i 507 . . . 4
71, 3, 63bitr4ri 271 . . 3
87abbii 2361 . 2
9 df-un 3083 . 2
10 df-iin 3806 . 2
118, 9, 103eqtr4i 2283 1
 Colors of variables: wff set class Syntax hints:   wo 359   wceq 1619   wcel 1621  cab 2239  wral 2509   cun 3076  cint 3760  ciin 3804 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-v 2729  df-un 3083  df-int 3761  df-iin 3806
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