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Theorem undir 3431
 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 3429 . 2
2 uncom 3332 . 2
3 uncom 3332 . . 3
4 uncom 3332 . . 3
53, 4ineq12i 3381 . 2
61, 2, 53eqtr4i 2326 1
 Colors of variables: wff set class Syntax hints:   wceq 1632   cun 3163   cin 3164 This theorem is referenced by:  undif1  3542  dfif4  3589  dfif5  3590  islimrs4  25685 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-in 3172
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