Answer
The law of detachment (or modus ponens)
Work Step by Step
Our task is to identify the rule(s) of inference used in the given argument.
Let's note the hypothesis by $p$:
$p$ = "Socrates is a man."
and by $q$ the conclusion:
$q$ = "Socrates is mortal."
The conditional statement is:
"If he is a man, then he is mortal."
Since the hypothesis and the conditional statement are both true, it follows that the conclusion is also true. The rule of inference used here is the law of detachment (or modus ponens) based on the tautology
$$(p\wedge(p\rightarrow q))\rightarrow q$$
