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I need to prove a few theorems about vector spaces using the axioms.

a) Prove: if -v = v, then v = 0

b) Prove: (-r)v = -(rv)

c) Prove: r(-v) = -(rv)

d) Prove: v - (-w) = v + w

where r is a scalar and v, w are vectors.

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# Prove a few theorems about vector spaces using the axioms

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