Provability Predicate as simple as possible

Conventional Propositional Logic proof :
(1) X
(2) Y
(3) (X ∧ Y) → Z
———–
(4) Z

Here is what the Propositional Logic proof means:
(1) X is True
(2) Y is True
(3) If (X and Y) are True then Z is True
(4) Therefore Z is True