let x1, x2, x3, x4, x5, x6, x7, x8 be object ; :: thesis: {x1,x2,x3,x4,x5,x6,x7,x8} = {x1,x2,x3,x4,x5} \/ {x6,x7,x8}
thus {x1,x2,x3,x4,x5,x6,x7,x8} = {x1,x2,x3,x4} \/ {x5,x6,x7,x8} by Lm6
.= {x1,x2,x3,x4} \/ ({x5} \/ {x6,x7,x8}) by Th4
.= ({x1,x2,x3,x4} \/ {x5}) \/ {x6,x7,x8} by XBOOLE_1:4
.= {x1,x2,x3,x4,x5} \/ {x6,x7,x8} by Th10 ; :: thesis: verum