Category has Finite Limits iff Finite Products and Equalizers

Theorem
Let $\mathbf C$ be a metacategory.

Then:


 * $\mathbf C$ has all finite limits

iff:


 * $\mathbf C$ has all finite products and equalizers.

Necessary Condition
By definition, finite products are instances of finite limits.

So are equalizers, by Equalizer as Limit.