Who sang the ABBA songs during movie Mamma Mia Actors or were they dubbed?

In the movie Mamma Mia!, actors Meryl Streep, Pierce Brosnan, Amanda Seyfried, and Dominic Cooper sang the ABBA songs. The only two songs that were not sung by the cast were "Gimme! Gimme! Gimme! (A Man After Midnight)" and "The Winner Takes It All", which were sung by the original ABBA singers, Agnetha Fältskog and Anni-Frid Lyngstad, respectively.