this is actually an interesting one. you usually see this as an axiom. not always, but a lot of the time.

....axiom (4)

.....distributive property

.......axiom (4)

i suppose you mean2) Ifxis any number, there do not exist two numbersyandy'such thatx*y= 1 andx*y'= 1.distinctnumbers y and y', of course.

assume to the contrary that there does exist distinct numbers y and y' such that

x*y = 1.........(a) and,

x*y' = 1 ........(b)

subtracting (b) from (a) we get

x*y - x*y' = 0

=> x(y - y') = 0

thus, x = 0 or y = y'

in either case, we have a contradiction. (do you see why? in particular, why does x = 0 yield a contradiction?)