Valid Baptism

Excerpt from "Reply to a Liberal III"

by Raymond Karam--http://catholicism.org/rptal-part3.html

(all reference numbers link back to original article) 

Is Baptism by Itself Sufficient for Salvation?
When is baptism valid?

1. When water is used.
2. When the proper words are used: “I baptize you in the name of the Father and of the Son and of the Holy Ghost.
3. If the person baptizing has the intention of doing what Christ intended, and
4. In the case of an adult being baptized, if the person baptized has the intention of receiving baptism.

For, as Pope Innocent III said,

But he who never consents but entirely contradicts, receives neither the res nor the character of the sacrament. 24

St. Thomas also says,

It must be said that if the intention of receiving the sacrament is lacking in an adult, he should be rebaptized. 25