No two electrons in an orbital can have parallel spin.  This statement emerges from

As per Pauli’s exclusion principle in an atom no two electrons can have all four quantum numbers to be same. It means two electrons with same n, l , ${\text{m}}_l$values have different ${\text{m}}_s$ values $-1/2\text{\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}+1/\hspace{0.17em}2}$.