Mediates the conversion of cyclohex-1-ene-1-carbonyl-CoA into (E)-2-cyclohex-1,5-diene-1-carbonyl-CoA in biosynthesis of cyclohexane-1-carboxylate, a by-product produced during fermentation of benzoate and crotonate to acetate. Also able to further convert (E)-2-cyclohex-1,5-diene-1-carbonyl-CoA to benzoyl-CoA. cyclohex-1-ene-1-carbonyl-CoA + H(+) + oxidized [electron-transfer flavoprotein] = cyclohexa-1,5-diene-1-carbonyl-CoA + reduced [electron-transfer flavoprotein] Homotetramer. Belongs to the acyl-CoA dehydrogenase family.