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Theorem undi 3323
 Description: Distributive law for union over intersection. Exercise 11 of [TakeutiZaring] p. 17. (Contributed by NM, 30-Sep-2002.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
undi

Proof of Theorem undi
StepHypRef Expression
1 elin 3266 . . . 4
21orbi2i 507 . . 3
3 ordi 837 . . 3
4 elin 3266 . . . 4
5 elun 3226 . . . . 5
6 elun 3226 . . . . 5
75, 6anbi12i 681 . . . 4
84, 7bitr2i 243 . . 3
92, 3, 83bitri 264 . 2
109uneqri 3227 1
 Colors of variables: wff set class Syntax hints:   wo 359   wa 360   wceq 1619   wcel 1621   cun 3076   cin 3077 This theorem is referenced by:  undir  3325  dfif4  3481  dfif5  3482 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-v 2729  df-un 3083  df-in 3085
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