Reduce boolean algebra

Question

I have to reduce this boolean algebra :

((x⊕y)⊕(y⊕z))⊕(x⊕(1⊕((y⊕0)⊕z)))

I found out that

1. ((x⊕y)⊕(y⊕z)) = x⊕z
2. y⊕0 = y
3. 1⊕(y⊕z) = negative(y⊕z)

looking at the solution it must be reducable to negative(y), but i don't know how to get from (x⊕z)⊕(x⊕negative(y⊕z)) to negative(y)

Answer 1

Next, note that we have $x\oplus \lnot(y\oplus z) = \lnot(x\oplus(y\oplus z))$. In fact, this $\lnot$ can be moved all the way to the front: $$ \lnot\big((x\oplus z)\oplus(x\oplus(y\oplus z))\big) $$ Lastly, note that $\oplus$ is both associative and commutative, so we can take away the parentheses and rearrange the terms to get $$ \lnot (x\oplus x \oplus y \oplus z \oplus z) = \lnot (0\oplus y \oplus 0) = \lnot y $$