In logic, do the $\Longrightarrow$ and $\rightarrow$ signify different things? In logic, do the $\Longrightarrow$ and $\rightarrow$ signify different things? Are there contexts where one is more appropriate than the other? I had believed that the $\Longrightarrow$ was for metalogic, and the $\rightarrow$ was for logic. However, recently, I've noticed $\Longrightarrow$ used more often than $\rightarrow$ in non-metalogical logical contexts.

Long story short, $\rightarrow$ is a logic operator, whereas $\implies$ is a statement (where you know the outcome must be true).

$\rightarrow$ : can have result "false". $\\\$ $\implies$ : Always true, by definition cannot be false. Not used as an operator.