The statement you’ve presented is a fundamental property of equality known as the substitution property.
To break it down:
- If we say that a = b, this implies that a and b are interchangeable in any statement or equation. Essentially, wherever you see ‘a’, you can replace it with ‘b’ and vice versa.
- Now, if it is also given that a = c, we can infer that since ‘a’ can be replaced by ‘b’ in the equality with ‘c’, we can rewrite it as b = c.
Thus, what this showcases is that if two numbers are equal to the same number, they must be equal to each other. This property is pivotal in mathematics, especially in algebra, as it allows us to manipulate and simplify expressions and equations.