let x1, x2, x3, x4, x5 be set ; :: thesis: {x1,x1,x2,x3,x4,x5} = {x1,x2,x3,x4,x5}
thus {x1,x1,x2,x3,x4,x5} = {x1,x1} \/ {x2,x3,x4,x5} by Th52
.= {x1} \/ {x2,x3,x4,x5} by Th69
.= {x1,x2,x3,x4,x5} by Th47 ; :: thesis: verum