I need to put the text as follows, but i don't see how.

Please help me.
\documentclass{article}
\usepackage{amsmath, amssymb}
\begin{document}
$$\llbracket \Phi_{1}(\vec{a})\wedge\Phi_{2}(\vec{a})\rrbracket \in U \textrm{ iff } \llbracket \Phi_{1}(\vec{a})\rrbracket\cap \llbracket\Phi_{2}(\vec{a})\rrbracket \in U$$
$$\textrm{ iff}$$
\end{document}
can not solve with \textrm

