A Proposal for a New Mathematical Symbol to Express "We Know That"

This paper presents a proposal for a new mathematical symbol to express the phrase “We know that” in mathematical proofs and solutions. In mathematical writing, symbols such as ∵ (Since) and ∴ (Therefore) are commonly used to express logical relationships. However, there is no widely established dedicated symbol specifically representing the introductory phrase “We know that”. This paper proposes a new symbol for this purpose, aiming to make mathematical proofs more concise, clear, and systematic. The proposed symbol is intended to indicate a known formula, theorem, mathematical rule, or generally accepted fact before its application in a proof. The paper explains the motivation behind the proposal, its possible applications, and its relationship with existing mathematical expressions. This is a proposed notation and is intended to invite discussion and further evaluation.