Theorem unvdif 3902

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
unvdif

Proof of Theorem unvdif

Step	Hyp	Ref	Expression
1		dfun3 3735	. 2
2		disjdif 3900	. . 3
3	2	difeq2i 3618	. 2
4		dif0 3898	. 2
5	1, 3, 4	3eqtri 2490	1

Syntax hints:  =wceq 1395  cvv 3109  \cdif 3472  u.cun 3473  i^icin 3474  c0 3784

This theorem is referenced by:  undif1  3903  dfif4  3956  hashf  12412  fullfunfnv  29596  hfext  29840

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785