Proving DeMorgan's Second Rule

[seto6]

Homework Statement

Hello, i proved the first demorgan's rule and using that i can easily proof the second one, but i tried to prove it as how i proved the first one. I would like to know what i did is correct, i feel i what i did might not be correct.

Homework Equations

(A $\cap$ B)^c = A^c $\cup$ B^c

proving through the fact that if;

A=B
then following two should be satisfiable:
A$\subset$B and B$\subset$A

The Attempt at a Solution

 

[micromass]

Seems correct!