p  q, q  r, r  p 

{

1. p -> q premise

2. q -> r premise

 3. ~r premise 

}

Complete the above proof using the following rules:  

example :

p  q  r, q  s, r  t  p  (t  s) { 1. p  q  r premise 2. { 3. p assume 4. q  r e 1 3 5. { 6. q assume 7. q  s premise 8. s e 7 6 9. t  s i2 8 } 10. { 11. r assume 12. r  t premise 13. t e 12 11 14. t V s Vi1 13 } 15. t  s e 4 5 10 } 16. p  (t  s) ->i 2 } 

PAQ PAQ And Rules i: Me1: e2: Or Rules: P assume Q assume vi1: ve: P V Q P assume Implies Rules: -i: P assume P assume Neg. Rules: : pbc