The triple bar, ≡, is a symbol used in formal logic

Logic

In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

. It has the appearance of a "=" sign with a third line.

Logically, it has a similar meaning to the if and only if

If and only if

In logic and related fields such as mathematics and philosophy, if and only if is a biconditional logical connective between statements....

 coupler ⇔. However, in some texts ⇔ is used as a symbol in logic formulas, while ≡ is for reasoning about those formulas (as in metalogic

Metalogic

Metalogic is the study of the metatheory of logic. While logic is the study of the manner in which logical systems can be used to decide the correctness of arguments, metalogic studies the properties of the logical systems themselves...

).

In addition, it has the completely separate meaning of modular congruence

Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus....

 in number theory: we write if N divides a − b.

This symbol is also used when it appears in an equation which is a definition of its left-hand side, that is an equation which is not derived but instead defined. Relatedly, it is used to signify an "identity

Identity (mathematics)

In mathematics, the term identity has several different important meanings:*An identity is a relation which is tautologically true. This means that whatever the number or value may be, the answer stays the same. For example, algebraically, this occurs if an equation is satisfied for all values of...

" - i.e. an equality that remains true regardless of the values of any variables that appear within.

It is also used for "identical equality" of functions; one writes for two functions f, g if we have for all x.

In chemistry

Chemistry

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, the triple bar can be used to represent a triple bond

Triple bond

A triple bond in chemistry is a chemical bond between two chemical elements involving six bonding electrons instead of the usual two in a covalent single bond. The most common triple bond, that between two carbon atoms, can be found in alkynes. Other functional groups containing a triple bond are...

 between atoms. For example, HC≡CH is a common short-hand for acetylene

Acetylene

Acetylene is the chemical compound with the formula C2H2. It is a hydrocarbon and the simplest alkyne. This colorless gas is widely used as a fuel and a chemical building block. It is unstable in pure form and thus is usually handled as a solution.As an alkyne, acetylene is unsaturated because...

.

The triple bar character in Unicode

Unicode

Unicode is a computing industry standard for the consistent encoding, representation and handling of text expressed in most of the world's writing systems...

 as codepoint . LaTeX

LaTeX

LaTeX is a document markup language and document preparation system for the TeX typesetting program. Within the typesetting system, its name is styled as . The term LaTeX refers only to the language in which documents are written, not to the editor used to write those documents. In order to...

\equiv corresponds to the triple bar.