We start with m < A + m < B = m < B + m < C as the given equation. We can rearrange the two terms on the right hand side to get m < A + m < B = m < C + m < B. From here, subtract m < B from both sides to end up with m < A = m < C. The angle B terms go away entirely. This rule I used was the subtraction property of equality. The next rule to use is the symmetric property to go from m < A = m < C to m < C = m < A. This rule is basically where we can flip the two sides of the equation and the equation is the same.
