Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  undir Unicode version

Theorem undir 3379
 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 3377 . 2
2 uncom 3280 . 2
3 uncom 3280 . . 3
4 uncom 3280 . . 3
53, 4ineq12i 3329 . 2
61, 2, 53eqtr4i 2286 1
 Colors of variables: wff set class Syntax hints:   wceq 1619   cun 3111   cin 3112 This theorem is referenced by:  undif1  3490  dfif4  3536  dfif5  3537  islimrs4  24935 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 1927  ax-ext 2237 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 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-v 2759  df-un 3118  df-in 3120
 Copyright terms: Public domain W3C validator