Mill's proof of the greatest happiness principle (step 3)
1. P6: Happiness is one of the ends of conduct.
2. P7: Happiness is one of the criteria for morality.
3. P8: Other elements (e.g. virtue, health and money) can be considered ends of conduct, but these are not universally agreed on.
4. P9: However these elements start as a means to gaining happiness for the person so, by association with happiness, they become ends in themselves.
5. P10: Through association, these elements become a part pf that person's happiness.
6. P11: This is the only way they become ends in themselves.
7. P12: Because these elements were initially sought as a means of happiness, happiness should be seen as the sole end of our conduct.