You don't need all those x's and (x)'s. They just get in
the way. And we know they're understood.
Use conditional proof or indirect proof as needed:
1. R ⊃ (T • ∼E)
2. (Q • R) ⊃ E / R ⊃ ∼Q
3. | R Assumption for Conditional proof
4. | T • ∼E 1,3, Modus Ponens
5. |~E • T 4, Commutation
6. |~E 5, Simplification
7. |~(Q • R) 2,6, Modus tollens
8. |~Q ∨ ~R 7, DeMordan's law
9. |~R ∨ ~Q 8, Commutation
10. |~~R 3, Double negation
11. |~Q 9,10, Disjunctive syllogism
12. R ⊃ ∼Q lines 3-11 Conditional proof
Edwin
