== Confusingly expressed == 

 Boltzmann himself used an expression equivalent to (3) in his later work[5] and recognized it as more general than equation (1). That is, equation (1) is a corollary of equation (3)—and not vice versa. In every situation where equation (1) is valid, equation (3) is valid also—and not vice versa. 

 The final sentence seems to say that (1) implies (3), which would contradict (1) being a corollary of (3). But I don't think think this is the intention. Please clarify.