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

Theorem undifv 3434
 Description: The union of a class and its complement is the universe. Theorem 5.1(5) of [Stoll] p. 17. (Contributed by NM, 17-Aug-2004.)
Assertion
Ref Expression
undifv

Proof of Theorem undifv
StepHypRef Expression
1 dfun3 3314 . 2
2 disjdif 3432 . . 3
32difeq2i 3208 . 2
4 dif0 3430 . 2
51, 3, 43eqtri 2277 1
 Colors of variables: wff set class Syntax hints:   wceq 1619  cvv 2727   cdif 3075   cun 3076   cin 3077  c0 3362 This theorem is referenced by:  undif1  3435  dfif4  3481  hashf  11222  fullfunfnv  23658  hfext  23987 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-ne 2414  df-ral 2513  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363
 Copyright terms: Public domain W3C validator