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Theorem iccf 13407
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 [,]:(ℝ* × ℝ*)⟶𝒫 ℝ*

Proof of Theorem iccf
Dummy variables 𝑥 𝑦 𝑧 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-icc 13313 . 2 [,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧𝑦)})
21ixxf 13316 1 [,]:(ℝ* × ℝ*)⟶𝒫 ℝ*
Colors of variables: wff setvar class
Syntax hints:  𝒫 cpw 4596   × cxp 5667  wf 6528  *cxr 11229  cle 11231  [,]cicc 13309
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2702  ax-sep 5292  ax-nul 5299  ax-pr 5420  ax-un 7708  ax-cnex 11148  ax-resscn 11149
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-nf 1786  df-sb 2068  df-mo 2533  df-eu 2562  df-clab 2709  df-cleq 2723  df-clel 2809  df-nfc 2884  df-ral 3061  df-rex 3070  df-rab 3432  df-v 3475  df-sbc 3774  df-csb 3890  df-dif 3947  df-un 3949  df-in 3951  df-ss 3961  df-nul 4319  df-if 4523  df-pw 4598  df-sn 4623  df-pr 4625  df-op 4629  df-uni 4902  df-iun 4992  df-br 5142  df-opab 5204  df-mpt 5225  df-id 5567  df-xp 5675  df-rel 5676  df-cnv 5677  df-co 5678  df-dm 5679  df-rn 5680  df-res 5681  df-ima 5682  df-iota 6484  df-fun 6534  df-fn 6535  df-f 6536  df-fv 6540  df-oprab 7397  df-mpo 7398  df-1st 7957  df-2nd 7958  df-xr 11234  df-icc 13313
This theorem is referenced by:  lecldbas  22652  ovolficc  24914  ovolficcss  24915  uniiccdif  25024  uniiccvol  25026  dyadmbllem  25045  dyadmbl  25046  opnmbllem  25047  opnmbllem0  36328  mblfinlem1  36329  mblfinlem2  36330
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