「 強い、 強い、 だめ、 だめ!」
The more interesting parts of maths lie where one can reach (apparently) strong results from (apparently) weak premises: yield to the desire to start with too strong of an antecedent, and your poor technique kills your own sword/[proper frame hom into 2]: ex falso quodlibet.
(look into your sword, Y. Gradstudent Sagiri: have you detached that head clause by cutting into a principal prime ideal and a completely prime filter?)