let W, x, y be set ; :: thesis: ( W is Tarski & x in W & y in W implies [x,y] in W )
assume A1:
W is Tarski
; :: thesis: ( not x in W or not y in W or [x,y] in W )
assume
( x in W & y in W )
; :: thesis: [x,y] in W
then
( {x} in W & {x,y} in W & [x,y] = {{x,y},{x}} )
by A1, Th3;
hence
[x,y] in W
by A1, Th3; :: thesis: verum