Use the Armstrong Rules $($IR$1$ through IR$3)$ to show all the steps to prove that the rule $($Rule IR$5)$ below is true. $\{xY,xZ\}||=x$ YZ$.$

$($That is: having $($using$)$ the left$-$hand side of $"\{xY,xZ\}",$ prove that the right$-$hand side of $"xYZ"$ is true.$)$

Note:

$1-$ This symbol $"1="$ is read as implies.

$2-$ To get the full points all the steps and details of computation need to be shown.