Suppose that the following statements are true:

(∃x)(A(x) ⇒ (∀y)(F(y) ⇒ C(y)))

(∃x)(B(x) ⇒ (∀y)(E(y) ⇒ ¬F(y)))

¬(∃x)(C(x) ∧ ¬E(x))

Then show using the laws of first-order logic that the following statement is true:

(∃x)(A(x) ∧ B(x)) ⇒¬(∃x)F(x)