First-countable and T1 implies cardinality at most of continuum

Statement
Any first-countable space that is also T1 has cardinality at most that of the continuum, i.e. the same as the cardinality of the continuum.

Proof
Given: A $$T_1$$-space $$X$$ that is first-countable

To prove: The cardinality of $$X$$ is at most equal to that of the continuum