take union {{x1,x2,x3,x4},{x5}} ; :: thesis: for x being object holds
( x in union {{x1,x2,x3,x4},{x5}} iff ( x = x1 or x = x2 or x = x3 or x = x4 or x = x5 ) )
let x be object ; :: thesis: ( x in union {{x1,x2,x3,x4},{x5}} iff ( x = x1 or x = x2 or x = x3 or x = x4 or x = x5 ) )
( x in {x1,x2,x3,x4} iff ( x = x1 or x = x2 or x = x3 or x = x4 ) ) by Def2;
hence ( x in union {{x1,x2,x3,x4},{x5}} iff ( x = x1 or x = x2 or x = x3 or x = x4 or x = x5 ) ) by Lm1; :: thesis: verum