defpred S₁[ set ] means ex x being set st
( x in UN & GO x,$1 );
for X1, X2 being set st ( for x being set holds
( x in X1 iff S₁[x] ) ) & ( for x being set holds
( x in X2 iff S₁[x] ) ) holds
X1 = X2 from XBOOLE_0:sch 3();
hence for b₁, b₂ being set st ( for y being set holds
( y in b₁ iff ex x being set st
( x in UN & GO x,y ) ) ) & ( for y being set holds
( y in b₂ iff ex x being set st
( x in UN & GO x,y ) ) ) holds
b₁ = b₂ ; :: thesis: verum