let G be non empty right_complementable add-associative right_zeroed addLoopStr ; :: thesis: for v, w being Element of G holds - ((- v) + w) = (- w) + v
let v, w be Element of G; :: thesis: - ((- v) + w) = (- w) + v
thus - ((- v) + w) = (- w) + (- (- v)) by RLVECT_1:31
.= (- w) + v by RLVECT_1:17 ; :: thesis: verum