When something is equal to something else, then they have the same value. For instance, if $y = 4$, then $y$ belongs to the set of numbers {4}. You are also able to use this to prove other statements.

Question: Given that $y = 4$, prove that $y^2 + y - 3 = 17$.

Solution: We can first square our original equation to get $y^2 = 16$. We can add $y$ to that, as we know that $y$ still equals $4$. So, $y^2 + y = 20$. We can also subtract both the left and the right side of the equation by $3$, giving us $y^2 + y - 3 = 17$. This proves what we wanted to prove.

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