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Theorem relbigcup 24437
Description: The  Bigcup relationship is a relationship. (Contributed by Scott Fenton, 11-Apr-2012.)
Assertion
Ref Expression
relbigcup  |-  Rel  Bigcup

Proof of Theorem relbigcup
StepHypRef Expression
1 relxp 4794 . . 3  |-  Rel  ( _V  X.  _V )
2 reldif 4805 . . 3  |-  ( Rel  ( _V  X.  _V )  ->  Rel  ( ( _V  X.  _V )  \  ran  ( ( _V  (x)  _E  )(++) ( (  _E  o.  _E  )  (x)  _V ) ) ) )
31, 2ax-mp 8 . 2  |-  Rel  (
( _V  X.  _V )  \  ran  ( ( _V  (x)  _E  )(++) ( (  _E  o.  _E  )  (x)  _V )
) )
4 df-bigcup 24399 . . 3  |-  Bigcup  =  ( ( _V  X.  _V )  \  ran  ( ( _V  (x)  _E  )(++) ( (  _E  o.  _E  )  (x)  _V )
) )
54releqi 4772 . 2  |-  ( Rel  Bigcup  <->  Rel  ( ( _V  X.  _V )  \  ran  (
( _V  (x)  _E  )(++) ( (  _E  o.  _E  )  (x)  _V )
) ) )
63, 5mpbir 200 1  |-  Rel  Bigcup
Colors of variables: wff set class
Syntax hints:   _Vcvv 2788    \ cdif 3149    _E cep 4303    X. cxp 4687   ran crn 4690    o. ccom 4693   Rel wrel 4694  (++)csymdif 24361    (x) ctxp 24373   Bigcupcbigcup 24377
This theorem is referenced by:  brbigcup  24438  dfbigcup2  24439
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-v 2790  df-dif 3155  df-in 3159  df-ss 3166  df-opab 4078  df-xp 4695  df-rel 4696  df-bigcup 24399
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