Given x = 1 and y = 1, then

x = y

Multiplying each side by x,

x² = xy

Subtracting y² from each side,

x² - y² = xy - y²

Factoring each side,

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

Dividing out the common term, (x - y) results in

x + y = y

Substituting the values of x and y,

1 + 1 = 1

or

2 = 1

"Q.E.D."