Theorem undisj1 3878

Description: The union of disjoint classes is disjoint. (Contributed by NM, 26-Sep-2004.)

Assertion

Ref	Expression
undisj1

Proof of Theorem undisj1

Step	Hyp	Ref	Expression
1		un00 3862	. 2
2		indir 3745	. . 3
3	2	eqeq1i 2464	. 2
4	1, 3	bitr4i 252	1

Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  u.cun 3473  i^icin 3474  c0 3784

This theorem is referenced by:  funtp  5645  f1oun2prg  12865

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-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785