There is something that I do not understand about the proof below. In the third line, the answer key says that they used the replacement property but I do not see how this is an application of the replacement property. For example, the replacement property is : $a = b$, thus $c + a$ can be rewritten as $c + b$. In the proof, they just added $-(a \cdot 0)$ on both sides which is mathematically correct but it doesn't seem like the replacement property to me. Can someone explain to me how adding $-(a \cdot 0)$ to both sides is the replacement? Thank you.
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Let $A= a\cdot 0 + a\cdot 0$, let $B = a\cdot 0$, and let $C= -(a\cdot 0)$.
Then the line in question is $A=B \implies A+C = B+C$, which is how you described the replacement property right?