let X1, X2 be set ; :: thesis: ( ( for x being set holds
( x in X1 iff ex g being Function st
( x = g & dom g = dom f & ( for y being set st y in dom f holds
g . y in f . y ) ) ) ) & ( for x being set holds
( x in X2 iff ex g being Function st
( x = g & dom g = dom f & ( for y being set st y in dom f holds
g . y in f . y ) ) ) ) implies X1 = X2 )
assume that
A18: for x being set holds
( x in X1 iff S₁[x] ) and
A19: for x being set holds
( x in X2 iff S₁[x] ) ; :: thesis: X1 = X2
thus X1 = X2 from XBOOLE_0:sch 2(A18, A19); :: thesis: verum