Is dog eating dog hair a two-part allegorical saying?

As the saying goes: dog bites dog, () mouth hair, is it one mouth hair or two mouth hairs? Where did this sentence come from?

Dog bites dog, full of hair.

This is a folk proverb. In order to read smoothly, the subject is omitted.

This sentence can be understood as follows: dog bites dog, and (no matter which dog) has a hair on its mouth.

Similar: whoever is late, the bonus will be deducted 50; A group of people went out without umbrellas and got wet.