let x1, x2, y1, y2, z be object ; :: thesis: ( z in [:{x1,x2},{y1,y2}:] implies ( ( z `1 = x1 or z `1 = x2 ) & ( z `2 = y1 or z `2 = y2 ) ) )
assume z in [:{x1,x2},{y1,y2}:] ; :: thesis: ( ( z `1 = x1 or z `1 = x2 ) & ( z `2 = y1 or z `2 = y2 ) )
then ( z `1 in {x1,x2} & z `2 in {y1,y2} ) by Th4;
hence ( ( z `1 = x1 or z `1 = x2 ) & ( z `2 = y1 or z `2 = y2 ) ) by TARSKI:def 2; :: thesis: verum