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Theorem intvlset 25698
Description: The set of intervals is a set. (Contributed by FL, 29-May-2014.)
Assertion
Ref Expression
intvlset  |-  Intvl  e.  _V

Proof of Theorem intvlset
StepHypRef Expression
1 df-intvl 25697 . 2  |-  Intvl  =  ( ( ran  (,)  u.  ( ran  (,]  u.  ( ran  [,)  u.  ran  [,] ) ) )  i^i 
~P RR )
2 reex 8828 . . . 4  |-  RR  e.  _V
32pwex 4193 . . 3  |-  ~P RR  e.  _V
43inex2 4156 . 2  |-  ( ( ran  (,)  u.  ( ran  (,]  u.  ( ran 
[,)  u.  ran  [,] )
) )  i^i  ~P RR )  e.  _V
51, 4eqeltri 2353 1  |-  Intvl  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1684   _Vcvv 2788    u. cun 3150    i^i cin 3151   ~Pcpw 3625   ran crn 4690   RRcr 8736   (,)cioo 10656   (,]cioc 10657   [,)cico 10658   [,]cicc 10659   Intvlcintvl 25696
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-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-pow 4188  ax-cnex 8793  ax-resscn 8794
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-in 3159  df-ss 3166  df-pw 3627  df-intvl 25697
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