let x be set ; :: thesis:
let f, g be Function; :: thesis:
thus pi {f,g},x c= {(f . x),(g . x)} :: according to XBOOLE_0:def 10 :: thesis:

let y be set ; :: according to TARSKI:def 3 :: thesis:
assume y in pi {f,g},x ; :: thesis:
then consider f1 being Function such that
A1: f1 in {f,g} and
A2: y = f1 . x by Def6;
( f1 = f or f1 = g ) by A1, TARSKI:def 2;
hence y in {(f . x),(g . x)} by A2, TARSKI:def 2; :: thesis:

end;