Metamath Proof Explorer

Theorem iccval

Description: Value of the closed interval function. (Contributed by NM, 24-Dec-2006) (Revised by Mario Carneiro, 3-Nov-2013)

Ref Expression
Assertion iccval 
|- ( ( A e. RR* /\ B e. RR* ) -> ( A [,] B ) = { x e. RR* | ( A <_ x /\ x <_ B ) } )

Proof

Step Hyp Ref Expression
1 df-icc 
 |-  [,] = ( y e. RR* , z e. RR* |-> { x e. RR* | ( y <_ x /\ x <_ z ) } )
2 1 ixxval 
 |-  ( ( A e. RR* /\ B e. RR* ) -> ( A [,] B ) = { x e. RR* | ( A <_ x /\ x <_ B ) } )