We prove a lower semicontinuity result for variational integrals associated with a given first order elliptic complex, extending, in this general setting, a well known result in the case ${}^{\text{'}}(ℝⁿ,ℝ){\to }^{\nabla }\text{'}(ℝⁿ,ℝⁿ){\to }^{curl}\text{'}(ℝⁿ,{ℝ}^{n\times n})$.