Proving Theorems in QL

Prove the following theorems. Click on selected problems for solutions.

1. (x)(Ax ⊃ Bx) ⊃ ((∃x)~Bx ⊃ (∃x)~Ax)
2. [(∃x)(Ax v Bx) & (x)~Bx] ⊃  [(∃x)Ax v (∃x)Bx]
3. (x)Sx ⊃ ((∃x)Tx ⊃ (x)Sx)
4. (~(∃x)Ax & ~(∃x)Bx) ⊃ (x)(Ax ⊃ Bx)
5. (x)(Ax & Bx) ⊃ ((x)Ax & (x)Bx)
6. (x)(Fx ⊃ Gx) ⊃ ((∃x)Fx ⊃ (∃x)Gx)