This is a question I was given in the exam: show that if $\lambda, \kappa$ are uncountable cardinals then $$(H_\lambda,\in) \prec_1 (H_\kappa,\in)$$ where $H_\lambda$ is the class of all sets $x$ such that $|TC(x)| < \lambda$. ($TC(x)$ refers to the transitive closure of $x$.)
Equivalently, given any $\Sigma_1$ formula $\varphi(x_1,x_2,...,x_n)$ with free variables shown and $a_1,a_2,...,a_n \in H_\lambda$ then $(H_\lambda,\in) \models \varphi(a_1,...,a_n)$ if and only if $(H_\kappa,\in) \models \varphi(a_1,...,a_n)$.
I have tried hard without success. Can anyone give me a hint?