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Im aware in vector spaces that there are 3 properties associated with it

Notevis an element in a vector space,0is the additive identity in the vector space and c is a field element

1) 0.v=0

2) c.0=0

3) (-c).v= c.(-.v) = -(c.v)

atm Im trying to prove 2), however I can only properly prove 2) if I use 1). As mathematical properties are meant to be unique, is my current solution considered as bad practice ?

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# Vector spaces + proving of properties

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