  There has been a proof by Sewell that the hypothesis of off-diagonal
long-range order in the reduced density matrix $\rho _2$ implies the Meissner
effect. We present in this note an elementary and straightforward proof that
not only the Meissner effect but also the property of magnetic flux
quantization follows from the hypothesis. It is explicitly shown that the two
phenomena are closely related, and phase coherence is the origin for both.
