A property of Boolean algebra

Question

In a Boolean algebra $\mathcal B$, we know that $$x+\bar{x}y=x+y\text{ for all } x, y\in \mathcal B.$$ By following the above identity, we can also write $$xy+\bar{x}yz=xy+yz.$$ Can we write $$\bar{y}xz+yp=xz+yp,\text{ where $p$ is distinct from $x$ and $z$}?$$ Or is there any alternative way to simplify the expression on the left side of the last equation further?

Answer 1

No. Taking $x = y = z = 1$ and $p = 0$, you get $\bar yxz +yp = 0$ but $xz + yp = 1$.