inheritance - In C#, if A implements IX and B inherits from A , does it necessarily follow that B implements IX? -

in c#, if implements ix , b inherits , follow b implements ix? if yes because of lsp ? there differences between :

1.

interface ix; class : ix; class b : a; 

and

2.

interface ix; class : ix; class b : a, ix; 

?

is there terminology associated b implementing ix though chain of inheritance or b implementing ix directly?

ps: assuming in both cases interface implemented implicitly, not explicitly. patterns utilize on 1 , not work if implemented in 2?

from msdn:

a class inherits interface implementations provided base classes. without explicitly re-implementing interface, derived class cannot in way alter interface mappings inherits base classes.

however, goes on if base class implements interface method virtual, can overridden derived class. implicit implementation can overridden in derived class explicitly.