I was reading Herrlich & Strecker's Category Theory, and there is a theorem called The Canonical construction of Pullbacks which states that if a category has products and equalizers, then it has pullbacks.
So I started to ask myself for some kind of converse. For instance, it is false that pullbacks and equalizers imply products, since the category of fields has pullbacks and equalizers but not products.
Then I asked if products and pullbacks imply equalizers. I haven't been able to come up with a counterexample, so I guess it must be true. Is there a proof of this?