Metamath Proof Explorer

Theorem icoval

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

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

Proof

Step Hyp Ref Expression
1 df-ico 
 |-  [,) = ( 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 ) } )