GCD: If $d\mid a, d\mid b$, and $d\mid c$, then $d|\mid \gcd(a,b,c)$

Question

How do I prove that If $d\mid a, d\mid b$, and $d\mid c$, then $d\mid \gcd(a,b,c)$ without using gcd(a,b,c)=gcd(gcd(a,b),c)?

I understand that the Common Divisor Divides GCD is only defined for two variables.