Show that: $$xy = (x|y)|(x|y)$$
I could get back from $(x|y)|(x|y)$ to $xy$, however, I can't seem to get it the other way around. This also looks a bit similar with $\neg x = x|x$. Is there a way to get from $xy$ to $(x|y)|(x|y)$?
Edit: $$(x|y)|(x|y)$$ $p|q = \neg(pq)$ $$\neg(xy)|\neg(xy)$$ $$\neg(\neg(xy)\neg(xy))$$ $pp = p$ $$\neg(\neg(xy))$$ $\neg \neg p = p$ $$xy$$
Thanks in advance.