Second-countable and T1 implies cardinality at most that of the continuum

Statement

Suppose a topological space is both a second-countable space and a T1 space. Then, its cardinality is at most equal to the cardinality of the continuum.

Facts used

1. Second-countable and T1 implies perfect
2. Perfect implies cardinality of space is at most the power cardinal of the cardinality of any basis

Proof

The proof follows directly by combining Facts (1) and (2).