( rng f c= D & rng g c= D )
by RELAT_1:def 19;

then A1: (rng f) \/ (rng g) c= D by XBOOLE_1:8;

rng (f ^ g) c= (rng f) \/ (rng g) by Th2;

hence rng (f ^ g) c= D by A1; :: according to RELAT_1:def 19 :: thesis: verum

then A1: (rng f) \/ (rng g) c= D by XBOOLE_1:8;

rng (f ^ g) c= (rng f) \/ (rng g) by Th2;

hence rng (f ^ g) c= D by A1; :: according to RELAT_1:def 19 :: thesis: verum