defpred S1[ Element of Aut G, Element of Aut G, set ] means $3 = $1 * $2;
A1: for x, y being Element of Aut G ex m being Element of Aut G st S1[x,y,m]
proof
let x, y be Element of Aut G; :: thesis: ex m being Element of Aut G st S1[x,y,m]
reconsider xx = x, yy = y as Homomorphism of G,G by Def1;
reconsider m = xx * yy as Element of Aut G by Th7;
take m ; :: thesis: S1[x,y,m]
thus S1[x,y,m] ; :: thesis: verum
end;
thus ex M being BinOp of (Aut G) st
for x, y being Element of Aut G holds S1[x,y,M . (x,y)] from BINOP_1:sch 3(A1); :: thesis: verum