Having trouble formulating proof...

I am completely new to proofs, so please bare with me.

I'm simply trying to prove that if $\displaystyle x\,<\,y\,\, then \,\,x^n\,<\,y^n\,\,for\,all\,odd\, n$

This seems simple enough, and i understand *why* it's true, but i'm having trouble expressing it in the form of a proof. I have that if x is greater than zero, then $\displaystyle x^n$ is also greater than zero. This is also true for all x greater than or less than zero provided that the number is raised to an even power. I reach this by arguing that the expression can always be reduced to factors of $\displaystyle x^2$ provided n is even, and thus the product is a product of positive numbers only. I *see* that the sign is preserved for odd n, which is the concept which underlies this proof, but i'm having trouble expressing it mathematically.

Could anyone help? Is there a good guide online somewhere regarding the formulation of basic proofs? The text I am working from is Spivak's Calculus (a great read) and I *am* able to follow his proofs, but this is the first time i've had to construct them myself. :)

Cheers,

John