thus ( f is pcs-yielding implies for x being set st x in dom f holds
f . x is pcs ) by FUNCT_1:3; :: thesis: ( ( for x being set st x in dom f holds
f . x is pcs ) implies f is pcs-yielding )
assume A2: for x being set st x in dom f holds
f . x is pcs ; :: thesis: f is pcs-yielding
let P be set ; :: according to PCS_0:def 29 :: thesis: ( P in rng f implies P is pcs )
assume P in rng f ; :: thesis: P is pcs
then ex x being object st
( x in dom f & f . x = P ) by FUNCT_1:def 3;
hence P is pcs by A2; :: thesis: verum