"Are these equivalent?" Protoman, sci.logic 1 ALL(x):[Human(x) => Mortal(x)] & EXIST(x):[Human(x) & Philosopher(x)] Premise 2 ALL(x):[Human(x) => Mortal(x)] Split, 1 3 EXIST(x):[Human(x) & Philosopher(x)] Split, 1 4 Human(a) & Philosopher(a) E Spec, 3 5 Human(a) Split, 4 6 Philosopher(a) Split, 4 7 Human(a) => Mortal(a) U Spec, 2 8 Mortal(a) Detach, 7, 5 9 Human(a) & Mortal(a) Join, 5, 8 10 Human(a) & Mortal(a) & Philosopher(a) Join, 9, 6 11 EXIST(x):[Human(x) & Mortal(x) & Philosopher(x)] E Gen, 10 12 ALL(x):[Human(x) => Mortal(x)] & EXIST(x):[Human(x) & Philosopher(x)] => EXIST(x):[Human(x) & Mortal(x) & Philosopher(x)] Conclusion, 1