Slaughtering "as I have commanded you"

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I love Rashi and can go on for days about his brilliance but I have to say that, l'ad, he gets it wrong on Deuteronomy 12:21:

"When the place which Hashem, your God, has chosen to place His name there, is distant from you and you will slaughter from your cattle and your herd which Hashem has given you, as I have commanded you, and you shall eat in your gates as all your soul desires." 

RASHI
And you will slaughter etc. as I have commanded you - RASHI: This teaches us that there is a command regarding slaughtering [animals to be eaten], how one should slaughter, and these must be the laws of slaughtering which were told to Moses at Sinai.

My point of disagreement is this: God has mentioned slaughtering earlier in the book. Perhaps our verse is not pointing to " laws of slaughtering which were told to Moses at Sinai.", ie,  the oral Torah, but to one of those instances. For example,  a mere five verses earlier we find a wider discussion of slaughtering.

And if you will say that the specific rules and details of slaughtering are not mentioned there either  I will reply that the written Torah never mentions such details. Our case - slaughtering - is merely another one of several cases of the Torah omitting to mention such rules details. If none of those other cases point to the existence of a second Torah neither does this one.

[Let me preempt your expected argument from consequences, please: I'm not looking to do anything other than understand the verse correctly; moreover my suggestion does nothing at all to "disprove" the existence of the Oral  Law. From the fact that this particular verse does not point at the Oral Torah, it does not follow that that there is no oral Torah. ]


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