(∀X)[Px ⊃ (∃Y)Rxy] ⊃ [(∀X)(∀y)∼Rxy ⊃ ∼(∃X)Px]

Multiple Choice

(∀x) [Px ⊃ (∃y) Rxy] ⊃ [(∀x) (∀y) ∼Rxy ⊃ ∼(∃x) Px]
-Consider assuming '(∀x) [Px ⊃ (∃y) Rxy]' for a conditional proof of the above logical truth. Which of the
Following propositions is a legitimate second step in that proof?

A) Assume '~(∃x) Px' for a nested conditional proof.
B) Assume '(∀x) (∀y) ∼Rxy' for a nested conditional proof.
C) Assume '~(∀x) (∀y) ~Rxy' for a nested indirect proof.
D) Px ⊃ (∃y) Ryy
E) Py ⊃ (∃y) Ryy