Formal logic proof using 19 rules of inference I am working on a problem in logic. The proof is supposed to involve only 19 rules of inference.
The problem is:
Given:
$$ Z \implies A $$
$$ Z \lor A $$
Deduce:
$$ A$$
My proof is 
$$ (Z \implies A) \land (Z \lor A) $$
$$ (Z \implies A) \land (\lnot \lnot Z \lor A) \text{(Double negation)}$$
$$ (Z \implies A) \land (\lnot Z \implies A) \text {(implication)} $$
$$ Z \lor \lnot Z \text{(tautology)} $$
$$ A \lor A \text {(constructive dilemma)} $$
$$ A \text{(tautology)} $$
What is my mistake?

I think that it would be much better illustrated as follows:
$ (Z \implies A) \land (Z \lor A) $
$ (\lnot Z \lor A) \land (Z \lor A) $
$ (A \lor \lnot Z) \land (A \lor Z) $
$ A \land (\lnot Z \lor Z) $
$ A \land true $
$ A $
