"to say nothing of " means not to even mention the importance of someone or something. Examples. 1. John and Mary had to be taken care of, to say nothing of Bill, who would require even more attention. 2. I'm having enough difficulty painting the house, to say nothing of the garage that is very much in need of paint. The idiom "dog eat dog" usually denotes furious competition for something (as in dog-eat-dog world). If you have ever seen two dogs fighting over a bone or tennis ball, then this phrase is obvious.

"Dog-eat-dog" describes a situation where people or groups are set against each other and there is almost no mercy shown. It is often used to describe the business world in areas where there is intense competition. "The electronics industry is dog-eat-dog. Many companies fail in their first year." "To say nothing of" means that something is so obvious that it need not be said. "There is danger to the company this next year of huge losses, to say nothing of complete failure.