set a = the Point of RAS;
let y, z be Vector of W; ( ( for a being Point of RAS holds y = Phi (a,x) ) & ( for a being Point of RAS holds z = Phi (a,x) ) implies y = z )
assume that
A1:
for a being Point of RAS holds y = Phi (a,x)
and
A2:
for a being Point of RAS holds z = Phi (a,x)
; y = z
y = Phi ( the Point of RAS,x)
by A1;
hence
y = z
by A2; verum