let x1, x2, x3 be set ; :: thesis: {x2,x1} \/ {x3,x1} = {x1,x2,x3}
thus {x2,x1} \/ {x3,x1} = {x2,x1,x3,x1} by Lm2
.= {x1,x1,x2,x3} by Th69
.= {x1,x2,x3} by Th31 ; :: thesis: verum