(Devarim 12:17) "and all your vows": This refers to burnt-offerings. What does Scripture come to teach us? If (that it is forbidden) to eat of a burnt-offering outside of the wall, this can be derived a fortiori from ma'aser. If (that it is forbidden) to eat of it before the sprinkling of blood, this can be derived a fortiori from sin and peace-offerings.
If (that it is forbidden to eat of it) after the sprinkling of its blood, this can be derived a fortiori from bechor. (If that it is forbidden to eat of it) outside the curtains, this can be derived from sin and guilt-offerings, viz.: If sin and guilt-offerings, which are permitted to be eaten — if one eats of them outside the curtains, he transgresses a positive commandment, then a burnt-offering, which is forbidden to be eaten — if one eats of it outside of the curtains, how much more so does he transgress a positive commandment!
The purpose of the verse, then, must be to teach us that if a Cohein eats of a burnt-offering, whether before or after the sprinkling of its blood, whether within or outside the curtains, he transgresses a negative commandment (for the burnt-offering must be completely burned).