Prove that if P$($n$),$ Q$($n$),$ R$($n$),$ f$($n$),$ g$($n$),$ h$($n$),$ and i$($n$)$ are all primitive recursive, then the function described as

if $!$P$($n$)$ then f$($n$)$ elseif $!$Q$($n$)$ then g$($n$)$ elseif $!$R$($n$)$ then h$($n$)$ else i$($n$)$

is also primitive recursive. Comment. Here, $!$P$,$ as usual in Java, means negation.