let p, q be Element of LTLB_WFF ; :: thesis: for X being Subset of LTLB_WFF st untn (p,q) in tau X holds
( p in tau X & q in tau X & p 'U' q in tau X )
let X be Subset of LTLB_WFF; :: thesis: ( untn (p,q) in tau X implies ( p in tau X & q in tau X & p 'U' q in tau X ) )
assume A1: untn (p,q) in tau X ; :: thesis: ( p in tau X & q in tau X & p 'U' q in tau X )
then p '&&' (p 'U' q) in tau X by Th21;
hence ( p in tau X & q in tau X & p 'U' q in tau X ) by A1, Th21, Th20; :: thesis: verum