Commentary for Leviticus 7:31

והקטיר הכהן את החלב AND THE PRIEST SHALL CAUSE THE FAT TO ASCEND IN FUMES [AT THE ALTAR] and only afterwards, והיה החזה לאהרן SHALL THE BREAST BE AARON’S [AND HIS SONS] — This teaches us that the flesh of the sacrifices may not be eaten so long as the fat portions are below the altar (have not yet been placed upon it and burnt) (Sifra, Tzav, Chapter 16 4; Pesachim 59b).