defpred S₃[ set ] means ex f being Function st
( f in X & $1 = f . x );
let X1, X2 be set ; :: thesis: ( ( for y being set holds
( y in X1 iff ex f being Function st
( f in X & y = f . x ) ) ) & ( for y being set holds
( y in X2 iff ex f being Function st
( f in X & y = f . x ) ) ) implies X1 = X2 )
assume that
A11: for y being set holds
( y in X1 iff S₃[y] ) and
A12: for y being set holds
( y in X2 iff S₃[y] ) ; :: thesis: X1 = X2
thus X1 = X2 from XBOOLE_0:sch 2(A11, A12); :: thesis: verum