let V be RealLinearSpace; for w, y being VECTOR of V
for a, b, c being Element of (DTrSpace (V,w,y)) st Gen w,y & a,b // b,c holds
( a = b & b = c )
let w, y be VECTOR of V; for a, b, c being Element of (DTrSpace (V,w,y)) st Gen w,y & a,b // b,c holds
( a = b & b = c )
let a, b, c be Element of (DTrSpace (V,w,y)); ( Gen w,y & a,b // b,c implies ( a = b & b = c ) )
assume that
A1:
Gen w,y
and
A2:
a,b // b,c
; ( a = b & b = c )
reconsider u = a, v = b, u1 = c as VECTOR of V ;
u,v,v,u1 are_DTr_wrt w,y
by A2, Th44;
hence
( a = b & b = c )
by A1, Th18; verum