defpred S₁[ object ] means $1 is Probability of S;
consider X being set such that
A1: for x being object holds
( x in X iff ( x in Funcs (S,REAL) & S₁[x] ) ) from XBOOLE_0:sch 1();
take X ; :: thesis: for x being object holds
( x in X iff x is Probability of S )
let x be object ; :: thesis: ( x in X iff x is Probability of S )
( x is Probability of S implies x in Funcs (S,REAL) ) by FUNCT_2:8;
hence ( x in X iff x is Probability of S ) by A1; :: thesis: verum