title: Antecedent (logic)
text: # 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:
  
  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.
  
  "$X$ is a man" is the antecedent for this proposition while "$X$ is mortal" is the consequent of the proposition.
  
  Here, "men have walked on the Moon" is the antecedent and "I am the king of France" is the consequent.
  
  Let $y=x+1$.
  
  "$x=1$" is the antecedent and "$y=2$" is the consequent of this hypothetical proposition.
  
  