There's a more general proof at https://docs.google.com/viewer?a=v&q=cache:euFgQLUCTfwJ:nm.mathforcollege.com/mws/gen/05inp/mws_gen_inp_bck_introduction.pdf+&hl

There's a more general proof at https://docs.google.com/viewer?a=v&q=cache:euFgQLUCTfwJ:nm.mathforcollege.com/mws/gen/05inp/mws_gen_inp_bck_introduction.pdf+&hl=en&gl=us&pid=bl&srcid=ADGEESg6HcId-jvRg7Ihh3dMF3DGTmBUCUOukBjCH1SunBJxGZFV3gri-zWyN91qUSinDMFJ3lvexKfgAvN3xewN2mWfG6idDKfHutuAcb62pH-UHJJXLUnbo3dCjt12NyTTYiZHuqDR&sig=AHIEtbSO9AURkaDNywKJ62dsSWklsecAEw https://docs.google.com/viewer?a=v&q=cache:euFgQLUCTfwJ:... that looks reasonable at a skim.