Metamath Proof Explorer

Theorem letopon

Description: The topology of the extended reals. (Contributed by Mario Carneiro, 3-Sep-2015)

Ref Expression
Assertion letopon 
|- ( ordTop ` <_ ) e. ( TopOn ` RR* )

Proof

Step Hyp Ref Expression
1 letsr 
 |-  <_ e. TosetRel
2 ledm 
 |-  RR* = dom <_
3 2 ordttopon 
 |-  ( <_ e. TosetRel -> ( ordTop ` <_ ) e. ( TopOn ` RR* ) )
4 1 3 ax-mp 
 |-  ( ordTop ` <_ ) e. ( TopOn ` RR* )