Proofs in Polyadic QL - Solutions

7. (x)((Tx & Sx) ⊃ Lax),  (∃x)~(~Tx v ~Sx) // (∃x)Lax

 

Proof:

1. (x)((Tx & Sx) ⊃ Lax) premise  
2. (∃x)~(~Tx v ~Sx) premise  
3. ~(~Tb v ~Sb) E.I., 2, flag b  
4. (Tb & Sb) ⊃ Lab) U.I., 1  
5. ~~Tb & ~~Sb DEM, 3  
6. Tb & ~~Sb D.N., 5  
7. Tb & Sb D.N. 6  
8. Lab M.P., 4, 7  
9. (∃x)Lax E.G., 8