The name of $p\Longrightarrow q \equiv \neg p \lor q$ logical equivalence

Question

As we now the negation of the conditional statement $p\Longrightarrow q$ is $p\land\neg q$. Using De Morgan Law then we get: $$p\Longrightarrow q \equiv \neg p \lor q.$$ Do you know if there is any name for this logical equivalence?

Answer 1

Philosophers call the equivalence $p \rightarrow q \Leftrightarrow \neg p \vee q$ the material implication rule.

One should not confuse this with the material conditional operation, which we also sometimes call the material implication operation: this is just the name of the usual $\rightarrow$ connective itself.

In the usual (so-called classical) logic that we use in everyday mathematics, the material implication operation $\rightarrow$ obeys the material implication rule. But in certain alternative logical systems, for example in the intuitionistic logic literature, $\rightarrow$ is still often called material implication, even though it does not obey the material implication rule!