Antecedent (logic)

An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause. In some contexts the antecedent is called the protasis.
Examples:

If, then.

This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is P, and the consequent is Q. In the implication " implies ", is called the antecedent and is called the consequent. Antecedent and consequent are connected via logical connective to form a proposition.

If is a man, then is mortal.

" is a man" is the antecedent for this proposition while " is mortal" is the consequent of the proposition.

If men have walked on the Moon, then I am the king of France.

Here, "men have walked on the Moon" is the antecedent and "I am the king of France" is the consequent.
Let.

If then.

"" is the antecedent and "" is the consequent of this hypothetical proposition.