"Want to demonstrate that this is a 'heresy'?"
Want to explain how the Catholic faith can "subsist" in false religions? The Modernists change "consist" to "subsist", which denies the requirement of being a member of the Catholic church to be saved, as I will quote the end of The Athanasian Creed: "This is the Catholic Faith, which except a man believe faithfully and firmly, he cannot be saved."
So how can the Church "subsist" in a religion that is outside of the only true religion where salvation can be attained?
Want to explain where the Catholic Church teaches that? In fact:
The interpretation of those who would derive from the formula subsistit in the thesis that the one Church of Christ could subsist also in non-Catholic Churches and ecclesial communities is therefore contrary to the authentic meaning of Lumen gentium. (Congregation for the Doctrine of the Faith, Dominus Iesus)