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Theorem reluni 4808
 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 3955 . . 3
21releqi 4772 . 2
3 reliun 4806 . 2
42, 3bitri 240 1
 Colors of variables: wff set class Syntax hints:   wb 176  wral 2543  cuni 3827  ciun 3905   wrel 4694 This theorem is referenced by:  fununi  5316  tfrlem6  6398  wfrlem6  24261  frrlem5b  24286  frrlem6  24290  bnj1379  28863 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-v 2790  df-in 3159  df-ss 3166  df-uni 3828  df-iun 3907  df-rel 4696
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