let X, x, Y be set ; (pi X,x) \+\ (pi Y,x) c= pi (X \+\ Y),x
A1:
(pi X,x) \ (pi Y,x) c= pi (X \ Y),x
by Th29;
A2:
(pi Y,x) \ (pi X,x) c= pi (Y \ X),x
by Th29;
(pi (X \ Y),x) \/ (pi (Y \ X),x) = pi ((X \ Y) \/ (Y \ X)),x
by Th27;
hence
(pi X,x) \+\ (pi Y,x) c= pi (X \+\ Y),x
by A1, A2, XBOOLE_1:13; verum