# How to express joint conditional probability with multiple conditions

I want to express the joint probability of $\Phi_A$ and $\Phi_B$: $p(\Phi_A, \Phi_B)$ conditioned that $\Phi_A$ and $\Phi_B$ are both greater than some value C. How would I express this mathematically? I guess my intuition says:

$p(\Phi_A, \Phi_B | \bf{\Phi} >C)$

Is this correct? Is there a better way to express this?

$p(\Phi_A, \Phi_B \; |\; \Phi_A>C \,\cap \Phi_B > C)$
Your current notation is not clear as $\Phi$ is not defined and not obvious what it means.