To show that a non-abelian group has elements a,b and c such that xy = yz and x≠z,

Would this be the correct approach?

For some x, y in a non-abelian group G

xy≠yx

and if

xy = yz for some z in G

then x≠z otherwise

xy≠yx

Is not satisfied for elements x and y of the group.

Is more detail required?

I feel like it is too straight forward

Thanks in advance