# Antecedent (logic) explained

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]}

Examples:

, 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.

is a man, then

is mortal.

"

is a man" is the antecedent for this 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.

Let

. If

then

## See also

## Notes and References

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