let x1, x2, x3, y1, y2, y3 be set ; :: thesis: proj1 (proj1 {[x1,x2,x3],[y1,y2,y3]}) = {x1,y1}
set X = {[x1,x2,x3],[y1,y2,y3]};
reconsider X = {[x1,x2,x3],[y1,y2,y3]} as Relation ;
thus proj1 (proj1 {[x1,x2,x3],[y1,y2,y3]}) = proj1 {[x1,x2],[y1,y2]} by RELAT_1:24
.= {x1,y1} by RELAT_1:24 ; :: thesis: verum