now :: thesis: for phi being wff string of S st phi in X \/ Y holds
I -TruthEval phi = 1

let phi be wff string of S; :: thesis: ( phi in X \/ Y implies I -TruthEval phi = 1 )
assume phi in X \/ Y ; :: thesis: I -TruthEval phi = 1
then ( phi in X or phi in Y ) by XBOOLE_0:def 3;
hence I -TruthEval phi = 1 by Def41; :: thesis: verum

end;

hence X \/ Y is I -satisfied ; :: thesis: verum