The second identity

If A = B and B = C, then A = C

A balances B, and B balances C. So A balances C too: A and C each weigh the same as B.

Two things that are each equal to the same thing are equal to each other.

This identity is called the transitive property of equality.

Transitive means it carries across: the equality goes from A through B to C. We write it if a = b and b = c, then a = c.

OK