defpred S₁[ set ] means ex f being Function of V,V st
( f = $1 & f is isometric );
thus 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(); :: thesis: verum