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 Th3
.= {x1,x2} \/ ({x3} \/ {x4,x5}) by XBOOLE_1:4
.= {x1,x2} \/ {x3,x4,x5} by Th2 ; :: thesis: verum