defpred S₁[ Element of UAAut UA, Element of UAAut UA, set ] means $3 = $2 * $1;
A1: for x, y being Element of UAAut UA ex m being Element of UAAut UA st S₁[x,y,m]

proof

let x, y be Element of UAAut UA; :: thesis: ex m being Element of UAAut UA st S₁[x,y,m]
reconsider xx = x, yy = y as Function of UA,UA ;
reconsider m = yy * xx as Element of UAAut UA by Th6;
take m ; :: thesis: S₁[x,y,m]
thus S₁[x,y,m] ; :: thesis: verum

end;

thus ex IT being BinOp of (UAAut UA) st
for x, y being Element of UAAut UA holds S₁[x,y,IT . (x,y)] from BINOP_1:sch 3(A1); :: thesis: verum