let x1, x2, x3, x4, x5 be object ; :: thesis: {x1,x2,x3,x4,x5} = {x1,x2,x3,x4} \/ {x5}
thus {x1,x2,x3,x4,x5} = {x1,x2,x3} \/ {x4,x5} by Lm3
.= {x1,x2,x3} \/ ({x4} \/ {x5}) by Th1
.= ({x1,x2,x3} \/ {x4}) \/ {x5} by XBOOLE_1:4
.= {x1,x2,x3,x4} \/ {x5} by Th6 ; :: thesis: verum