let T be non empty pathwise_connected TopSpace; for y0, y1 being Point of T holds pi_1 (T,y0), pi_1 (T,y1) are_isomorphic
let y0, y1 be Point of T; pi_1 (T,y0), pi_1 (T,y1) are_isomorphic
set R = the Path of y1,y0;
take
pi_1-iso the Path of y1,y0
; GROUP_6:def 11 pi_1-iso the Path of y1,y0 is bijective
thus
pi_1-iso the Path of y1,y0 is bijective
; verum