Theorem relun 5124

Description: The union of two relations is a relation. Compare Exercise 5 of [TakeutiZaring] p. 25. (Contributed by NM, 12-Aug-1994.)

Assertion

Ref	Expression
relun

Proof of Theorem relun

Step	Hyp	Ref	Expression
1		unss 3677	. 2
2		df-rel 5011	. . 3
3		df-rel 5011	. . 3
4	2, 3	anbi12i 697	. 2
5		df-rel 5011	. 2
6	1, 4, 5	3bitr4ri 278	1

Syntax hints:  <->wb 184  /\wa 369  cvv 3109  u.cun 3473  C_wss 3475  X.cxp 5002  Relwrel 5009

This theorem is referenced by:  difxp  5436  funun  5635  fununfun  5637

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-un 3480  df-in 3482  df-ss 3489  df-rel 5011