Premises:
∀x∀y(P(x,y) ↔ Q(y))
∀x∀y(Q(x,y) ↔ R(x,y))

Conclusion:
∀x∀y(P(x,y) ↔ R(x,y))

1    ∀x∀y (P(x, y) ↔ Q(y))                   Premiss
2    ∀x∀y (Q(x, y) ↔ R(y))                   Premiss
3    ∀y (P(x, y) ↔ Q(y))                     1 (∀E)
4    (P(x, y) ↔ Q(y))                        3 (∀E)
5    ∀y (Q(x, y) ↔ R(y))                     2 (∀E)
6    (Q(x, y) ↔ R(y))                        5 (∀E)
7    (P(x, y) → Q(y))                        4 (↔E)
..... don't know how to keep going...

Premises:
∀x∀y(P(x,y)→Q(x,y))
∀x(Q(x,1) V R(1))

Conclusion:
∀xƎy(Q(x,y) V R(y))