Definition:Only If

Definition

To say that:

a statement $p$ is true only if $q$ is true

is to say that:

$p$ is a sufficient condition for $q$:

Thus:

$p \ \text{only if} \ q \dashv \vdash p \implies q$

Also see

• Definition:If

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): only if