let X be set ; :: thesis: for Y being complex-functions-membered set
for f being PartFunc of X,Y
for g being complex-valued Function holds dom (f <-> g) = (dom f) /\ (dom g)
let Y be complex-functions-membered set ; :: thesis: for f being PartFunc of X,Y
for g being complex-valued Function holds dom (f <-> g) = (dom f) /\ (dom g)
let f be PartFunc of X,Y; :: thesis: for g being complex-valued Function holds dom (f <-> g) = (dom f) /\ (dom g)
let g be complex-valued Function; :: thesis: dom (f <-> g) = (dom f) /\ (dom g)
thus dom (f <-> g) = (dom f) /\ (dom (- g)) by Def41
.= (dom f) /\ (dom g) by VALUED_1:8 ; :: thesis: verum