Can someone check are my proofs correct?

Theorem 1:If there are two intersecting lines $\displaystyle p$ and $\displaystyle q$ which are parallel to plane $\displaystyle \alpha $, then lines $\displaystyle p$ and $\displaystyle q$ determines plane $\displaystyle \beta $ which is parallel to plane $\displaystyle \alpha $.

Proof:Lines $\displaystyle p$ and $\displaystyle q$ determines plane $\displaystyle \beta $ which doesn't have common points with $\displaystyle \alpha $ so if $\displaystyle \alpha \cap \beta = \emptyset $ then planes $\displaystyle \alpha $ and $\displaystyle \beta $ are parallel.

Theorem 2:Through given point $\displaystyle B$ there is only one plane that is parallel to given plane $\displaystyle \alpha $.

Proof:Lets say that plane $\displaystyle \beta $ goes through point $\displaystyle B$ which is parallel to plane $\displaystyle \alpha $. If there is another plane for example $\displaystyle \beta' $ that would go through point $\displaystyle B$ which is parallel to plane $\displaystyle \alpha $ then it would be $\displaystyle \beta' = \beta $.