A quantum-statistical binary gas mixture model consisting of positive-energy resonant bosonic Cooper electron pairs in chemical and thermal equilibrium with single unpaired electrons yields, via two-time retarded Green functions, an analytic expression for a dimensionless coupling λ- and temperature T-dependent generalized energy gap Eg(λ, T) in the single-electron spectrum. The new gap gives a reasonable description of overdoped Bi2Sr2CuO6+δ (Bi2201).