"a dream come true"

"Our vacation by the ocean was a dream come true."

I have learned that a dream come true is used as a one chunk and a noun phrase and is this just an idiom or could you analyze it?

For example,

a dream (that has) come true

a dream (that is) come true
.
.
However, these are not common ways of omitting and using so I am confused. What do you native English speakers think?

Thank you so much in advance.