let X, Y, Z be set ; :: thesis: for f being Function of X,Y
for g being Function of X,Z holds rng <:f,g:> c= [:Y,Z:]
let f be Function of X,Y; :: thesis: for g being Function of X,Z holds rng <:f,g:> c= [:Y,Z:]
let g be Function of X,Z; :: thesis: rng <:f,g:> c= [:Y,Z:]
( rng f c= Y & rng g c= Z ) by RELAT_1:def 19;
then A1: [:(rng f),(rng g):] c= [:Y,Z:] by ZFMISC_1:96;
rng <:f,g:> c= [:(rng f),(rng g):] by Th51;
hence rng <:f,g:> c= [:Y,Z:] by A1; :: thesis: verum