Is the division property of equality just a special case of the multiplication property? My textbook clearly states after the lesson on Transforming Equations: Addition and Subtraction
"Notice that the subtraction property of equality is just a special case of the addition property, since subtracting the number c is the same as adding -c."
But, following the next lesson which is on Transforming Equations: Multiplication and Division there is no equivalent statement such as 
The division property of equality is just a special case of the multiplication property, since dividing by the number c is the same as multiplying by the reciprocal of c. 
Is division just a special case of multiplication, with the restriction of not having 0 in the denominator?
If so, why would they not include such a  natural parallel statement?

If the book is not very "symmetric" in general, it's possible that they just kind of forgot it or something. However, my guess is that the book is aimed at beginners, and it's easy for them to forget that zero is a special case, especially when variables are used. For me it's easier to remember to check for zero when I'm thinking of dividing instead of multiplying by the reciprocal. So, suppose I have
$$ac=bc.$$
If I learn that I can just multiply by the reciprocal of $c$ I would get
$$a=b$$
which is not necessarily true. However, if I think that I could divide by $c$, I'll probably remember that zero is always an exception and I would get
$$a=b\quad\text{or}\quad c=0$$
which is correct. Of course you can learn that zero is an exception in the multiply-by-reciprocal case, too, but I think that the division-by-zero problem is more deeply planted already.
