Difference between $\equiv$ and $=$? What is the difference between $\equiv$ and $=$?
My thought is, that, when $\equiv$ is used $=$ could have been used as well. The resulting expression would not be wrong, but just take on a slightly different meaning. But what exactly is the relation between those symbols?
To give a practical example, consider those:
$$
=:⟺∀:(x∈\iff∈)
$$
$$
=:=∀:(x∈\iff∈)
$$
$$
=:\equiv∀:(x∈\iff∈)
$$
Or those:
$$
5+7=12
$$
$$
5+7\equiv12
$$
$$
5+7=7+5
$$
$$
5+7\equiv7+5
$$

$\equiv$ is used for $\text{identity}$ mostly, but $=$ is used for equation
