Deriving a conclusion from two premises, only one of which is quantified

Question

I have these premises:

1. $\forall x:S(x)\to E(x)$
2. $S(x)\land D(x),$

and this conclusion: $\exists x:E(x)\land D(x).$

I'm having a hard time figuring out how to use rule(s) of inference to derive the conclusion.

Answer 1

Premise 1 says: For every object, if that object has property S, then it also has property E.

Premise 2 says: The object named $x$ has property S and property D.

The conclusion says: There is some object that has property $E$ and property $D$.

Do you understand intuitively why the conclusion follows from the premises?

The intuitive reasoning translates into a formal proof like this: Apply the first premise to the object named $x$ (universal instantiation), then prove that the object named $x$ has the desired two properties (a few propositional steps), then "forget the name of $x$ but remember that it exists" (existential introduction).