 In other words, \(x\) is an element of \(y\) just in case \(x\) falls under a concept of which \(y\) is the extension. For example, given this definition, one can prove that John is a member of the extension of the concept being happy (formally: \(j \in \epsilon H)\) from the premise that John falls under the concept being happy (‘\(Hj\)’). Here is a simple proof: 