# 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 $P$ , then $Q$ .

This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is P, and the consequent is Q. In an implication, if $\phi$ implies $\psi$ then $\phi$ is called the antecedent and $\psi$ is called the consequent. Antecedent and consequent are connected via logical connective to form a proposition.

• If $X$ is a man, then $X$ is mortal.

"$X$ is a man" is the antecedent for this proposition while "$X$ 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 $y=x+1$ .

• If $x=1$ then $y=2$ ,.

"$x=1$ " is the antecedent and "$y=2$ " is the consequent of this hypothetical proposition.