Consider a number
a. By the ,
a is equal to itself.
a=a
Let
b be another number. If
b is added to and from the left-hand side of the above , the equality still holds true.
a=a⇔a+b−b=a
Finally,
b−b is equal to
0.
a+b−b=a⇔a+0=a ✓
It has been shown that
a+0=a. By the ,
0+a is also equal to
a.