Checking for language containment between nondeterministic ω-automata is a central task in automata-based hierarchical verification. We present a symbolic procedure for language containment checking between two Büuchi automata. Our algorithm avoids determinization by intersecting the implementation automaton with the complement of the specification automaton as an alternating automaton. We present a fix-point algorithm for the emptiness check of alternating automata. The main data structure is a nondeterministic extension of binary decision diagrams that canonically represents sets of Boolean functions.