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Mirrors > Home > ILE Home > Th. List > iccf | GIF version |
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.) |
Ref | Expression |
---|---|
iccf | ⊢ [,]:(ℝ* × ℝ*)⟶𝒫 ℝ* |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-icc 9920 | . 2 ⊢ [,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 ≤ 𝑧 ∧ 𝑧 ≤ 𝑦)}) | |
2 | 1 | ixxf 9923 | 1 ⊢ [,]:(ℝ* × ℝ*)⟶𝒫 ℝ* |
Colors of variables: wff set class |
Syntax hints: 𝒫 cpw 3590 × cxp 4639 ⟶wf 5228 ℝ*cxr 8016 ≤ cle 8018 [,]cicc 9916 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4189 ax-pr 4224 ax-un 4448 ax-cnex 7927 ax-resscn 7928 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-sbc 2978 df-csb 3073 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-iun 3903 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4308 df-xp 4647 df-rel 4648 df-cnv 4649 df-co 4650 df-dm 4651 df-rn 4652 df-res 4653 df-ima 4654 df-iota 5193 df-fun 5234 df-fn 5235 df-f 5236 df-fv 5240 df-oprab 5896 df-mpo 5897 df-1st 6160 df-2nd 6161 df-pnf 8019 df-mnf 8020 df-xr 8021 df-icc 9920 |
This theorem is referenced by: (None) |
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