let x be set ; :: thesis: for p, q being ExtReal st x in ].p,q.[ holds
( x in ].p,q.] & x <> q )
let p, q be ExtReal; :: thesis: ( x in ].p,q.[ implies ( x in ].p,q.] & x <> q ) )
assume A1: x in ].p,q.[ ; :: thesis: ( x in ].p,q.] & x <> q )
then reconsider s = x as ExtReal ;
A2: p < s by A1, Th4;
s < q by A1, Th4;
hence ( x in ].p,q.] & x <> q ) by A2, Th2; :: thesis: verum