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Theorem iccf 10758
Description: The set of closed intervals of extended reals maps to subsets of extended reals. (Contributed by FL, 14-Jun-2007.) (Revised by Mario Carneiro, 3-Nov-2013.)
Assertion
Ref Expression
iccf  |-  [,] :
( RR*  X.  RR* ) --> ~P RR*

Proof of Theorem iccf
Dummy variables  x  y  z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-icc 10679 . 2  |-  [,]  =  ( x  e.  RR* ,  y  e.  RR*  |->  { z  e.  RR*  |  (
x  <_  z  /\  z  <_  y ) } )
21ixxf 10682 1  |-  [,] :
( RR*  X.  RR* ) --> ~P RR*
Colors of variables: wff set class
Syntax hints:   ~Pcpw 3638    X. cxp 4703   -->wf 5267   RR*cxr 8882    <_ cle 8884   [,]cicc 10675
This theorem is referenced by:  lecldbas  16965  ovolficc  18844  ovolficcss  18845  uniiccdif  18949  uniiccvol  18951  dyadmbllem  18970  dyadmbl  18971  opnmbllem  18972  bsi2  25742
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-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pow 4204  ax-pr 4230  ax-un 4528  ax-cnex 8809  ax-resscn 8810
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-sbc 3005  df-csb 3095  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-pw 3640  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-iun 3923  df-br 4040  df-opab 4094  df-mpt 4095  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-rn 4716  df-res 4717  df-ima 4718  df-iota 5235  df-fun 5273  df-fn 5274  df-f 5275  df-fv 5279  df-oprab 5878  df-mpt2 5879  df-1st 6138  df-2nd 6139  df-xr 8887  df-icc 10679
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