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Metamath Proof Explorer

Theorem mstps

Description: A metric space is a topological space. (Contributed by Mario Carneiro, 26-Aug-2015)

Ref Expression
Assertion mstps 
|- ( M e. MetSp -> M e. TopSp )

Proof

Step Hyp Ref Expression
1 msxms 
 |-  ( M e. MetSp -> M e. *MetSp )
2 xmstps 
 |-  ( M e. *MetSp -> M e. TopSp )
3 1 2 syl 
 |-  ( M e. MetSp -> M e. TopSp )