let x1, x2, x3 be set ; :: thesis: {x1,x1,x2,x3} = {x1,x2,x3}
thus {x1,x1,x2,x3} = {x1,x1} \/ {x2,x3} by Lm2
.= {x1} \/ {x2,x3} by Th69
.= {x1,x2,x3} by Th42 ; :: thesis: verum