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Theorem intvlset 25801
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 25800 . 2  |-  Intvl  =  ( ( ran  (,)  u.  ( ran  (,]  u.  ( ran  [,)  u.  ran  [,] ) ) )  i^i 
~P RR )
2 reex 8844 . . . 4  |-  RR  e.  _V
32pwex 4209 . . 3  |-  ~P RR  e.  _V
43inex2 4172 . 2  |-  ( ( ran  (,)  u.  ( ran  (,]  u.  ( ran 
[,)  u.  ran  [,] )
) )  i^i  ~P RR )  e.  _V
51, 4eqeltri 2366 1  |-  Intvl  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1696   _Vcvv 2801    u. cun 3163    i^i cin 3164   ~Pcpw 3638   ran crn 4706   RRcr 8752   (,)cioo 10672   (,]cioc 10673   [,)cico 10674   [,]cicc 10675   Intvlcintvl 25799
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-pow 4204  ax-cnex 8809  ax-resscn 8810
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-ss 3179  df-pw 3640  df-intvl 25800
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