thus ( f is pcs-Str-yielding implies for x being set st x in dom f holds
f . x is pcs-Str ) by FUNCT_1:3; :: thesis: ( ( for x being set st x in dom f holds
f . x is pcs-Str ) implies f is pcs-Str-yielding )
assume A1: for x being set st x in dom f holds
f . x is pcs-Str ; :: thesis: f is pcs-Str-yielding
let P be set ; :: according to PCS_0:def 28 :: thesis: ( P in rng f implies P is pcs-Str )
assume P in rng f ; :: thesis: P is pcs-Str
then ex x being object st
( x in dom f & f . x = P ) by FUNCT_1:def 3;
hence P is pcs-Str by A1; :: thesis: verum