let X be non empty TopSpace; for X0, X1 being non empty SubSpace of X st X0 misses X1 holds
(modid (X,X0)) | X1 is continuous Function of X1,(X modified_with_respect_to X0)
let X0, X1 be non empty SubSpace of X; ( X0 misses X1 implies (modid (X,X0)) | X1 is continuous Function of X1,(X modified_with_respect_to X0) )
assume
X0 misses X1
; (modid (X,X0)) | X1 is continuous Function of X1,(X modified_with_respect_to X0)
then
for x1 being Point of X1 holds (modid (X,X0)) | X1 is_continuous_at x1
by Th106;
hence
(modid (X,X0)) | X1 is continuous Function of X1,(X modified_with_respect_to X0)
by Th44; verum