It works for me if I complete your code to create a minimal example:
\documentclass{article}
\usepackage{amssymb}
\usepackage{amsmath}
\begin{document}
\[
L1 \cap Li \neq \Phi
\]
\end{document}

Admittedly, this isn't yet quite right because it does not look quite like the target set of symbols.
To obtain a subscript in a mathematical expression, just use L_{<subscript>}
. To obtain the lowercase Greek letter, use \phi
rather than \Phi
.
\[
L_1 \cap L_i \neq \phi
\]

EDIT
In light of Heiko Oberdiek's comment, for the final symbol, I'm not entirely clear which one you want but I suspect that Heiko may be right. In any case, here's a selection to choose from:
\[
\phi \Phi \varphi \emptyset \varnothing
\]

\[...\]
$ ... $
around your equation, or\( ... \)
. Try$\mathbf{L}_{1} \cap \mathbf{L}_{i} \neq \mathbf{\Phi}$
\[ ... \]
will also work, although that will enter a displayed maths environment. Use\[ ... \]
for displayed maths and$ ... $
or\( ... \)
for in-line maths\Phi
is probably quite wrong and the symbol means the empty set instead.