let x be set ; :: thesis: for p, q being ExtReal st x in ].p,q.[ holds
( x in [.p,q.] & x <> p & x <> q )
let p, q be ExtReal; :: thesis: ( x in ].p,q.[ implies ( x in [.p,q.] & x <> p & x <> q ) )
assume A1: x in ].p,q.[ ; :: thesis: ( x in [.p,q.] & x <> p & x <> q )
then x in ].p,q.] by Th15;
hence ( x in [.p,q.] & x <> p & x <> q ) by A1, Th12, Th15; :: thesis: verum