  An argument is valid in a model just when in any point at which the premises are true, so is the conclusion. The argument \(A \vdash B \rightarrow B\) is invalid because we may have a point \(x\) at which \(A\) is true, but at which \(B \rightarrow B\) is not.  We can have \(B \rightarrow B\) fail to be true at \(x\) simply by having \(Rxyz\) where \(B\) is true at \(y\) but not at \(z\). 