set c = the carrier of G;
defpred S1[ Element of G, set ] means $2 = * $1;
A1: for x being Element of G ex y being Element of (SymGroup the carrier of G) st S1[x,y]
proof
let x be Element of G; :: thesis: ex y being Element of (SymGroup the carrier of G) st S1[x,y]
set y = * x;
* x in permutations the carrier of G ;
then reconsider y = * x as Element of (SymGroup the carrier of G) by Def2;
take y ; :: thesis: S1[x,y]
thus S1[x,y] ; :: thesis: verum
end;
ex f being Function of G,(SymGroup the carrier of G) st
for x being Element of G holds S1[x,f . x] from FUNCT_2:sch 3(A1);
 hence ex b1 being Function of G,(SymGroup the carrier of G) st
for g being Element of G holds b1 . g = * g ; :: thesis: verum