The Logic Book, M. Bergmann, J. Moor, J. Nelson, McGraw Hill, 2004, 10.4E, 1(j), p. 555

We are asked to derive the conclusion from the premises given.

1. (y)(x)(Cxy ⊃ Qx)
2. (y)(Qy ≡ Py)
3. ∴(y)(x)(Cxy ⊃Px)
4. (x)(Cxy ⊃ Qx) ......... 1 UI y/y
5. Cxy ⊃ Qx ......... 4 UI x/x
6. Qx ≡ Px ......... 2 UI y/x
7. (Qx ⊃ Px) • (Px ⊃ Qx) ......... 6 BE
8. Qx ⊃ Px ......... 7 Simp.
9. Cxy ⊃Px ......... 5,8 HS
10. (x)(Cxy ⊃Px) ......... 9 UG
11. (y)(x)(Cxy ⊃Px) ......... 10 UG