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Theorem undir 3746
 Description: Distributive law for union over intersection. Theorem 29 of [Suppes] p. 27. (Contributed by NM, 30-Sep-2002.)
Assertion
Ref Expression
undir

Proof of Theorem undir
StepHypRef Expression
1 undi 3744 . 2
2 uncom 3647 . 2
3 uncom 3647 . . 3
4 uncom 3647 . . 3
53, 4ineq12i 3697 . 2
61, 2, 53eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395  u.cun 3473  i^icin 3474 This theorem is referenced by:  undif1  3903  dfif4  3956  dfif5  3957  bwth  19910 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-in 3482
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