let x1, x2, x3 be set ; :: thesis: card {x1,x2,x3} <= 3
( card {x1} = 1 & {x1,x2,x3} = {x1} \/ {x2,x3} & {x1} is finite & {x2,x3} is finite & card {x2,x3} <= 2 ) by Th69, CARD_1:50, ENUMSET1:42;
then ( 1 + (card {x2,x3}) <= 1 + 2 & card {x1,x2,x3} <= 1 + (card {x2,x3}) ) by Th62, XREAL_1:9;
hence card {x1,x2,x3} <= 3 by XXREAL_0:2; :: thesis: verum