let x, y be object ; :: thesis: for X, Y being set st [x,y] in [:X,Y:] holds
[y,x] in [:Y,X:]
let X, Y be set ; :: thesis: ( [x,y] in [:X,Y:] implies [y,x] in [:Y,X:] )
( [x,y] in [:X,Y:] implies ( x in X & y in Y ) ) by Lm16;
hence ( [x,y] in [:X,Y:] implies [y,x] in [:Y,X:] ) by Lm16; :: thesis: verum