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## Homework Statement

Let x,y,and z be vectors in a vector space V. Prove that if x+y=x+z

then y=z

I know it cant be as simple as just subtracting vector x from both sides.

What i'm thinking is out goal is to get y=z which means that there much be a zero vector

in the relationship x+y=x+z.

My guess is that x is the zero vector in this case. I'm not that good with proofs yet, but I have been reading "How to prove it" so i split it up into givens and goals.

given is x,y,and z be vectors in a vector space V and x+y=x+z

goal being y=z.

am I allowed to grab one of the axioms as a staring point for the proof?