the denial of David Hume's existence implies a contradiction.

“There is no being whose non-existence implies a contradiction.”

—David Hume

Suppose that David Hume, whose name we shall abbreviate ‘h’, doesn’t exist. It follows that David Hume both exists and doesn’t—which is a contradiction.

                                    ∴ ¬(∃x)x = h ⊃ ((∃x)x = h • ¬(∃x)x = h)

1.         ¬(∃x)x = h      (assumption)

2.         h = h                (truism)

3.         (∃x)x = h         2, EG

4.         (∃x)x = h • ¬(∃x)x = h            1, 3, •I

5.    ¬(∃x)x = h  ⊃ ((∃x)x = h • ¬(∃x)x = h)    1-4, CP