the number of people who shake an odd number of other people's hands is even
... that whenever some of the people in a party shake hands, the number of people who shake an odd number of other people's hands is even?
... that whenever some of the people in a party shake hands, <b id="mwAU4"><a href="./Handshaking_lemma" id="mwAU8" rel="mw:WikiLink" title="Handshaking lemma">the number of people who shake an odd number of other people's hands is even</a></b>?