Rabbi Akiva offered his own proof that eating meat cooked in milk is forbidden, using a different a fortiori argument. His starting point was not the Passover offering but the thigh sinew — the gid hanasheh, the sciatic nerve that Jacob injured during his wrestling match with the angel.
The thigh sinew is forbidden to eat (Genesis 32:33), but it is not forbidden to cook. You may cook it — you simply may not eat it. Now consider meat and milk: it is explicitly forbidden to cook them together. If the thigh sinew, which lacks a cooking prohibition, still has an eating prohibition, then meat and milk — which has a cooking prohibition — must certainly have an eating prohibition as well.
Rabbi Akiva's reasoning parallels the argument from the Passover offering but uses a different example. Both proofs arrive at the same conclusion: the eating of meat cooked in milk is forbidden even though the Torah states only the cooking prohibition explicitly.
The availability of two independent a fortiori arguments strengthens the conclusion. The eating prohibition is not derived from a single chain of reasoning that might be challenged. It is established through multiple converging logical paths. Whether you reason from the Passover offering or from the thigh sinew, you arrive at the same place: if cooking is forbidden, eating must be forbidden too. The Torah's silence on eating is not a gap — it is an invitation to reason.