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