Complete the logical proof for the following argument.

AAx$(P(x)Q(x))$

EEx$(R(x{)}^{{?}^{?}}P(x))$

:$.$EEx$(R(x{)}^{{?}^{?}}Q(x))$

$\backslash$table$[[$Step$,$Proposition,Justification$],[1,$EEx$(R(x{)}^{{?}^{?}}P(x)),$Hypothesis$],[2,c$ is a specific element ${?}^{{?}^{?}}(R(c{)}^{{?}^{?}}P(c)),$Universal ins tan tiation, $1],[3,c$ is a specific element,Simplification, $2],[4,R(c{)}^{{?}^{?}}P(c),$Simplification, $2],[5,$AAx$(P(x)Q(x)),$Hypothesis$],[6,P(c)Q(c),$Universal ins tan tiation, $4],[7,P(c),$Simplification, $4],[8,Q(c),$Modus Ponens, $6,7],[9,R(c),$Simplification, $4],[10,,$Conjunction $8,9],[11,$EEx$(R(x{)}^{{?}^{?}}Q(x)),$Universal generalization, $10]]$

Note that the justification for each step is either hypothesis or it would include both the name of the law or rule and the step$($s$)$ to which it is applied to$.$

Copy and paste the logical operators when filling in the blanks: $v,{}_1,$not,$AA,EE.$