Your emergency fund should only be used for a large unexpected expense for which you have not otherwise budgeted.
Typically the main purpose is to support some level of reduced living expenses in case you lose your job. The reduction should cut out the frills but allow you to maintain a reasonable semblance of your existing lifestyle.
So you should probably stop going out to eat, buying new clothes, or going on vacation. However, continue eating well and paying for education, your mortgage, insurance policies, etc.
Other emergencies for which you might use these funds are a large, infrequent and unexpected medical expense or auto repairs.
If an expense happens frequently or regularly it should be built into your cash flow plan so that you save some of your income on an ongoing basis to pay for it.
Anytime you withdraw from your emergency fund you should make it a top priority to start rebuilding it to its prior level as soon as possible.
Even if you can only afford a small deposit weekly start doing so immediately.
If you are saving towards other goals you should redirect some or all of these ongoing savings to rebuild your emergency fund so you are ready for the next emergency.