However, it is necessary to have an emergency fund after buying the investment. If a person spends 80% of his discretionary income on his daily living expenses, then from the remaining 20%, he should invest 10% and 10% for emergency fund. It is a misconception that you do not have to have an emergency fund.
You are misunderstanding what discretionary income is. A discretionary income is the extra leftover money from your income after you must have taken care of your basic needs and monthly expenses. It's your discretionary income that you are to use to invest in bitcoin in order for you to be able to hodli for long. Your income is what you use to take care of your basic needs and monthly expenses.
You can make your discretionary income 50% on bitcoin, 50% on emergency funds at the start. However, if you feel pressured to buy BTC while you have an emergency fund, the best decision would be to immediately close the emergency fund and focus on buying Bitcoin.
If you have already started your bitcoin journey and have set up your emergency funds, whenever you don't home discretionary income, there is no amount of pressure that should make you use close down your emergency funds and use all of it to invest into bitcoin because emergency funds is the back up to your bitcoin investment should incase you are hit with an unforeseen circumstances. You don't have to sell your bitcoin but use your emergency funds to solve it.
If you use all your emergency funds to buy bitcoin due to pressure like you said, you are only risking your investment to sell it prematurely because when you are hit with real life emergency, you will use your bitcoin investment as your emergency funds and sell at loss if bitcoin price is below your entry point. No long-term bitcoin investor should neglect the importance of emergency funds to the point of closing it down and use it to buy bitcoin because it means that you are only gambling.