Exists

Exists[x, expr] represents the statement that there exists a value of x for which expr is True.

Exists[x, cond, expr] states that there exists an x satisfying the condition cond for which expr is True.

Exists[{x1, x2, ...}, expr] states that there exist values for all the xi for which expr is True.

Examples

Check for existence:

Resolve[Exists[x, x^2 == 4]]
(* True *)

Existence with a condition:

Resolve[Exists[x, x > 0, x^2 == 4]]
(* True *)

Please visit the official Wolfram Language Reference for more details.