# Denying the antecedent

**Denying the antecedent**is a type of logical fallacy.

Suppose in an argument one were to deny the "if" part of a conditional (the antecedent) first, and conclude with the denial of "then" part (the consequent).

- If P, then Q.
- P is false.
- Therefore, Q is false.

*denying the antecedent,*because in arguing this way one does indeed deny the antecedent in the second premise. This is a non-sequitur. If we argue this way, we make a mistake. One can see this with an example:

- If there is fire here, then there is oxygen here. (Since oxygen is required for fire.)
- There is no fire here.
- Therefore, there is no oxygen here.

*if*and

*if and only if*. Denying the antecedent is valid if the first premise asserts "if and only if" rather than "if".

*See also:* modus ponens, modus tollens, affirming the consequent.