Dubious proofs, part one

Let

x = y

Then

x² = xy

Subtract y²:

x² - y² = xy - y²

Factorise:

(x + y)(x - y) = x(x - y)

A bit of cancelling gives us

x + y = x

Let x = y = 1, so

1 + 1 = 1

Convinced?