let n be Element of NAT ; :: thesis: for L being Element of line_of_REAL n ex x1, x2 being Element of REAL n st L = Line x1,x2
let L be Element of line_of_REAL n; :: thesis: ex x1, x2 being Element of REAL n st L = Line x1,x2
L in line_of_REAL n
;
then consider L0 being Subset of (REAL n) such that
A1:
( L = L0 & ex x1, x2 being Element of REAL n st L0 = Line x1,x2 )
;
consider x1, x2 being Element of REAL n such that
A2:
L = Line x1,x2
by A1;
take
x1
; :: thesis: ex x2 being Element of REAL n st L = Line x1,x2
take
x2
; :: thesis: L = Line x1,x2
thus
L = Line x1,x2
by A2; :: thesis: verum