let x, X be set ; ( x in proj2_3 X implies ex y, z being set st [y,x,z] in X )
assume
x in proj2_3 X
; ex y, z being set st [y,x,z] in X
then consider y being set such that
W1:
[y,x] in proj1 X
by Def5;
consider z being set such that
W2:
[[y,x],z] in X
by W1, Def4;
take
y
; ex z being set st [y,x,z] in X
take
z
; [y,x,z] in X
thus
[y,x,z] in X
by W2; verum