let x1, x2, x3, x4 be set ; :: thesis: {x1,x2,x3,x4} = {x1} \/ {x2,x3,x4}
thus {x1,x2,x3,x4} = {x1,x2} \/ {x3,x4} by Lm2
.= ({x1} \/ {x2}) \/ {x3,x4} by Th41
.= {x1} \/ ({x2} \/ {x3,x4}) by XBOOLE_1:4
.= {x1} \/ {x2,x3,x4} by Th42 ; :: thesis: verum