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Theorem undifv 3694
 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 3571 . 2
2 disjdif 3692 . . 3
32difeq2i 3454 . 2
4 dif0 3690 . 2
51, 3, 43eqtri 2459 1
 Colors of variables: wff set class Syntax hints:   wceq 1652  cvv 2948   cdif 3309   cun 3310   cin 3311  c0 3620 This theorem is referenced by:  undif1  3695  dfif4  3742  hashf  11617  fullfunfnv  25783  hfext  26116 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621
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