Let our signature be that of a single binary operation $*$. I define $*$ to satisfy the constant identity if $x*y=z*w$. But, I am interested in another identity, this one: $x*y=y*z$. I want to know if it is equivalent to the constant identity. I think it is, but I don't know how to prove it.
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5Hint: what happens when you take the second identity twice, once with y in the middle and once with z, and then use transitivity of equality? – peabrainiac Jul 16 '23 at 19:56
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@peabrainiac Oh, you are right. I didn't see that before. – user107952 Jul 16 '23 at 20:02