Metamath Proof Explorer

Theorem cnxmet

Description: The absolute value metric is an extended metric. (Contributed by Mario Carneiro, 28-Aug-2015)

Ref Expression
Assertion cnxmet 
|- ( abs o. - ) e. ( *Met ` CC )

Proof

Step Hyp Ref Expression
1 cnmet 
 |-  ( abs o. - ) e. ( Met ` CC )
2 metxmet 
 |-  ( ( abs o. - ) e. ( Met ` CC ) -> ( abs o. - ) e. ( *Met ` CC ) )
3 1 2 ax-mp 
 |-  ( abs o. - ) e. ( *Met ` CC )