Metamath Proof Explorer


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
|- [,] : ( RR* X. RR* ) --> ~P RR*

Proof

Step Hyp Ref Expression
1 df-icc
 |-  [,] = ( x e. RR* , y e. RR* |-> { z e. RR* | ( x <_ z /\ z <_ y ) } )
2 1 ixxf
 |-  [,] : ( RR* X. RR* ) --> ~P RR*