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Theorem iccf 13036
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 12942 . 2 [,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧𝑦)})
21ixxf 12945 1 [,]:(ℝ* × ℝ*)⟶𝒫 ℝ*
Colors of variables: wff setvar class
Syntax hints:  𝒫 cpw 4513   × cxp 5549  wf 6376  *cxr 10866  cle 10868  [,]cicc 12938
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2158  ax-12 2175  ax-ext 2708  ax-sep 5192  ax-nul 5199  ax-pr 5322  ax-un 7523  ax-cnex 10785  ax-resscn 10786
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-nf 1792  df-sb 2071  df-mo 2539  df-eu 2568  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2886  df-ne 2941  df-ral 3066  df-rex 3067  df-rab 3070  df-v 3410  df-sbc 3695  df-csb 3812  df-dif 3869  df-un 3871  df-in 3873  df-ss 3883  df-nul 4238  df-if 4440  df-pw 4515  df-sn 4542  df-pr 4544  df-op 4548  df-uni 4820  df-iun 4906  df-br 5054  df-opab 5116  df-mpt 5136  df-id 5455  df-xp 5557  df-rel 5558  df-cnv 5559  df-co 5560  df-dm 5561  df-rn 5562  df-res 5563  df-ima 5564  df-iota 6338  df-fun 6382  df-fn 6383  df-f 6384  df-fv 6388  df-oprab 7217  df-mpo 7218  df-1st 7761  df-2nd 7762  df-xr 10871  df-icc 12942
This theorem is referenced by:  lecldbas  22116  ovolficc  24365  ovolficcss  24366  uniiccdif  24475  uniiccvol  24477  dyadmbllem  24496  dyadmbl  24497  opnmbllem  24498  opnmbllem0  35550  mblfinlem1  35551  mblfinlem2  35552
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