It's in the papal bull.
Or encyclical, if you prefer.
That is not part of the definition of the Immaculate Conception, but rather, the concept of Mary being the Mediatrix of grace, which is NOT part of the definition. Notice in the Ineffabilis Deus, Pope Pius IX gives the explanations for the doctrine. Here is the definition:
"We declare, pronounce, and define that the doctrine which holds that the most Blessed Virgin Mary, in the first instance of her conception, by a singular grace and privilege granted by Almighty God, in view of the merits of Jesus Christ, the Savior of the human race, was preserved free from all stain of original sin, is a doctrine revealed by God and therefore to be believed firmly and constantly by all the faithful."
Nothing about what you are talking about.
Regards