Your emergency fund covers vet bills up to a value of $3,000. This is available to you one time per year. However, if your vet bill is less than $3,000, you will not be credited the difference and you will have used your emergency fund for the year.
For example, if after your emergency your vet bill is $100, you can choose to pay $100 upfront and out-of-pocket in order to preserve your $3,000 for a larger and more expensive emergency. If you decide to use the emergency fund for a $100 vet bill, you will not be credited the remaining balance, and you will not be able to use the fund again that year.