dog tastes a lot like chicken (everything does)

Lemma: All chickens taste the same (by induction).

Proof: It's obvious that one chicken tastes the same. Let us assume th proposition P(k) that k chickens taste the same & how this is to imply that k + 1 chickens taste the same.
Given the st k + 1, we remove 1 chicken; the remaining k chickens all taste the same, by hypothesis. We remove another chicken & replace the first; the k chickens, by hypothesis, are again the same flavour. We repeat this, until (by exhaustion) the k + 1 sets of k chickens have been shown to taste the same.
It follows then that since every chicken is the same flavour as every other chicken, P(k) entails P(k + 1). But since we have shown P(1) to be true, P is true for all succeding values of k; ie all chickens taste the same.

Corollary I: Everything tastes the same.

Proof: The proof of the above lemma does not depend on the nature of the object under consideration. The precedate of the antecedant of the universally-quantified conditional “For all x, if x is a chicken, then x all taste the same.”, namely ‘is a chicken’ may be generalised to ‘is anything’ without affecting the validity of the proof. Hence, “For all x, if x is anything, x all taste the same.”
(Incedentally, x all taste the same even if x isn't anything. I'll leave the proof to you.)

Corollary II: Everything tastes of chicken.

Proof: If a sential formula in x is logically true, then any particular substitution instance of it is a true statement. In particular, then “For all x, if x is a dog, then x all taste the same.” is true. Now it is manifestly axiomatic that an amount of dogs greater than 0 taste of chicken. (For proof by blatant assertion, consult Gnolam.) Therefore, by corollary I, everything tastes of chicken.

Q.E.D.