x1 is a logical 'NOT' statement resulting from the (multiplicative) negation of/applying the 'NOT' operator to x2 (du'u); x1 is the logical negation/negative of x2.
x1 is a material conditional/'IF' statement (logical statement) saying that x2 (du'u) logically implies x3 (du'u) ("x3 is true if x2 is true; if x2, then x3; x2 being true is sufficient to guarantee the truth of x3").
x1 is a logical statement of proposition-equivalence/is a biconditional/'IFF' statement saying that x2 (du'u) is true if and only if x3 is true ("x2 is logically equivalent to x3; x2 being true is sufficient and necessary for guaranteeing the truth of x3; x2 iff x3").