I have been given a question by my tutor to try out for our next class(adsbygoogle = window.adsbygoogle || []).push({});

Using the axioms for addition of numbers give a natural language proof that the additive inverse of a number is unique, that is prove:

∀x∀y∀z (x + y = 0) ^ (x + z = 0) → (y = z)

I am new at writing proofs!

My attempt

1. x + y = 0 premis

2. x + (-x) +y = (-x)

3. 0 + y = -x

4. y = -x

5. x + z = 0 premis

6. z = -x

7. (y = -x) ^ (z = -x) --> x = z transivity axiom

therefore (x + y = 0) ^ (x + z = 0) → (y = z) by ded principle line 4, 6

I think this right, but as it's one of my first proofs I am unsure if this is enough...

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# Natural Language proof of additive inverse

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