Antecedent (logic)

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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.[1]


  • If , then .

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 implies then is called the antecedent and is called the consequent.[2] 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.

See also[edit]


  1. ^ See Conditional sentence.
  2. ^ Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004