In the propositional logic, let the string $(a_1, a_2, \cdots, a_n)$ be WFF. And exist natural numbers $i< j\in \{1,2 \cdots, n\}$ search that string $(a_i,a_{i+1}, \cdots , a_j )$ is also WFF. Prove that if $(b_1, b_2, \cdots, b_m)$ is WFF, then $(a_1, a_2, a_{i-1}, b_1, b_2, \cdots, b_m, a_{j+1}\cdots, a_n)$ is also WFF.
In my logical book, substitution is defined only for proposition letter. But I think this is true. How can we prove this?