Numbers equal zero

Theorem : All numbers are equal to zero.

Proof: Let that a=b. Then
a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a + b)(a - b) = b(a - b)
a + b = b
a = 0

Furthermore if a + b = b, and a = b (given) , then b + b = b, and 2b = b, which mean that 2 = 1.

Here the fallacy is in the 4th step .

If 4*0 = 5*0 , we cannot say that 4 = 5 by cancelling zeros .