Premise or Given - ∃x(A(x) → B(x)) ∀x (B(x) → K(x)) To Prove - ∃x(A(x) → K(x)) My Solution - 1) A(z) → B(z) From premise and Existential instantiation x for z 2) B(z) → K(z) From premise and Universal instantiation x for z 3) A(z) → K(z) Transitivity of 1,2 4)∃x(A(x) → K(x)) From Existential Generalization Substitute z for x Am I doing this right if not is there any other way to prove it ? Login To add answer/comment