:: deftheorem Def3 defines chi FUNCT_3:def 3 :
for A, X being set
for b₃ being Function holds
( b₃ = chi (A,X) iff ( dom b₃ = X & ( for x being object st x in X holds
( ( x in A implies b₃ . x = 1 ) & ( not x in A implies b₃ . x = 0 ) ) ) ) );