Strictly Equivalent To

The four-line equivalence symbol marks strict equivalence under a defined relation. The writer’s definitions say which relation; the bars alone do not specify it.

The three-line ≡ is a different glyph. Gauss used it for modular congruence in 1801: numbers leave the same remainder when divided by the same integer. That history belongs to the three-line sign; it does not date ≣ or establish a shared origin.

Use ≣ only when the definition calls for it

Treat ≣ as notation specific to the text or mathematical field using it. In a paper or textbook formula, look for the author’s definition; in your own writing, use this mark only if your chosen convention calls for it.