How to denote a one to one mapping between $A = { B,C,D}$ and $B = { {X_1},{X_2},{X_3}}$?

How to denote there exist a one to one mapping with order between the set $A = { B,C,D}$ and the set $B = { {X_1},{X_2},{X_3}}$ ?

Particularly, the result will be like this:

$begin{gathered}
B = {X_1} hfill \
C = {X_2} hfill \
D = {X_3} hfill \
end{gathered}$

Is there any way to write this compactly instead of listing each and every element like this because sometime the cardinal of both sets can be large.

Please help me,

Thank you for your enthusiasm !