Metamath Proof Explorer

Theorem ngptps

Description: A normed group is a topological space. (Contributed by Mario Carneiro, 5-Oct-2015)

Ref Expression
Assertion ngptps 
|- ( G e. NrmGrp -> G e. TopSp )

Proof

Step Hyp Ref Expression
1 ngpms 
 |-  ( G e. NrmGrp -> G e. MetSp )
2 mstps 
 |-  ( G e. MetSp -> G e. TopSp )
3 1 2 syl 
 |-  ( G e. NrmGrp -> G e. TopSp )