let x1, x2, x3, x4 be object ; :: 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 Th1
.= ({x1,x2} \/ {x3}) \/ {x4} by XBOOLE_1:4
.= {x1,x2,x3} \/ {x4} by Th3 ; :: thesis: verum