defpred S₁[ set ] means ( $1 in X & $1 is Function );
let X1, X2 be set ; :: thesis: ( ( for x being set holds
( x in X1 iff ( x in X & x is Function ) ) ) & ( for x being set holds
( x in X2 iff ( x in X & x is Function ) ) ) implies X1 = X2 )
assume that
A1: for x being set holds
( x in X1 iff S₁[x] ) and
A2: for x being set holds
( x in X2 iff S₁[x] ) ; :: thesis: X1 = X2
thus X1 = X2 from XBOOLE_0:sch 2(A1, A2); :: thesis: verum