let X be set ; :: thesis: for f being X -valued Function
for x being set st x in dom f holds
f . x in X
let f be X -valued Function; :: thesis: for x being set st x in dom f holds
f . x in X
let x be set ; :: thesis: ( x in dom f implies f . x in X )
assume x in dom f ; :: thesis: f . x in X
then A1: f . x in rng f by Def3;
rng f c= X by RELAT_1:def 19;
hence f . x in X by A1; :: thesis: verum