Theorem iccf

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
Assertion	iccf	$$⊢\left[.\right]:{ℝ}^{*}\times {ℝ}^{*}⟶𝒫{ℝ}^{*}$$

Proof

Step	Hyp	Ref	Expression
1		df-icc	$$⊢\left[.\right]=\left(x\in {ℝ}^{*},y\in {ℝ}^{*}⟼\left\{z\in {ℝ}^{*}|\left(x\le z\wedge z\le y\right)\right\}\right)$$
2	1	ixxf	$$⊢\left[.\right]:{ℝ}^{*}\times {ℝ}^{*}⟶𝒫{ℝ}^{*}$$