We give a self contained proof of a logarithmic lower bound on the communication complexity of any non redundant function, given that there is no access to shared randomness. This bound was first stated in Yao's seminal paper [STOC 1979], but no full proof appears in the literature.

Our proof uses the method of Babai and Kimmel [Computational Complexity 1997], introduced there in the context of the simultaneous messages model, applying it to the more general and standard communication model of Yao.