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Theorem undifv 3624
 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 3493 . 2
2 disjdif 3622 . . 3
32difeq2i 3382 . 2
4 dif0 3620 . 2
51, 3, 43eqtri 2377 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642  cvv 2859   cdif 3206   cun 3207   cin 3208  c0 3550 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551 This theorem is referenced by:  undif1  3625  dfif4  3673
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