Rules of inference for quantified statements
Universal instantiation: ---------
Existential generalization: --------
- All Canny integers are non-Slotty
- All Bumpy integers are Slotty
- There is an integer that is not Bumpy
1. ?x(C(x) ? ? S(x)) Axiom
2. C(3) ? ? S(3) From 1 by Universal instantiation
4. ? S(3) From 2,3 by Modus ponens
6. B(3) ? S(3) From 5 by Universal instantiation
7. ? B(3) From 4,6 by Modus tollens
8. ?x ? B(x) From 7 by Existential generalization