Given $$\forall x.(p(x) \implies q(x))\quad and \quad p(a)$$ use the Fitch system to prove q(a)
I have started: $$\\$$
$$1) \forall X.(p(X) \implies q(X)) \qquad (Premise)$$
$$2) p(a) \qquad (Premise)$$
$$3) \exists X.p(X) \qquad (Existential \quad Introduction:2)$$
$$\\$$ but I do not know how to continue. I believe I must prove also $$\forall x.(p(x) \implies q(a))$$ and by existential elimination I will get q(a). Can anyone help?
You need, at line 3, to instantiate the universal quantifier with the only available constant ...
The fact that you ask this exceedingly elementary question here suggests that you badly need to do some basic reading to get the hang of deductions in predicate logic: try e.g. Paul Teller's treatment of a Fitch-style system in his freely available Modern Primer. which has lots of worked examples clearly explained.