The relevance of a rule’s antecedent for the rule’s consequent
In our conception of rules, a rule’s antecedent can be adduced as a reason for the rule’s consequent.
This implies that a rule’s antecedent is in some sense relevant for the rule’s consequent: the antecedent gives support for the consequent.
If John is a thief, then he is punishable.
If John is a thief, then it rains.