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Theorem reluni 5130
Description: The union of a class is a relation iff any member is a relation. Exercise 6 of [TakeutiZaring] p. 25 and its converse. (Contributed by NM, 13-Aug-2004.)
Assertion
Ref Expression
reluni
Distinct variable group:   ,

Proof of Theorem reluni
StepHypRef Expression
1 uniiun 4383 . . 3
21releqi 5091 . 2
3 reliun 5128 . 2
42, 3bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  A.wral 2807  U.cuni 4249  U_ciun 4330  Relwrel 5009
This theorem is referenced by:  fununi  5659  tfrlem6  7070  wfrlem6  29348  frrlem5b  29392  frrlem6  29396  bnj1379  33889
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-ral 2812  df-rex 2813  df-v 3111  df-in 3482  df-ss 3489  df-uni 4250  df-iun 4332  df-rel 5011
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