Source SSH from A through B to C, using private key on A
ssh -o ProxyCommand="ssh -i path_to_private_key -W %h:%p A" -i path_to_private_key B
Source SSH from A through B to C, using private key on A
ssh -o ProxyCommand="ssh -i path_to_private_key -W %h:%p A" -i path_to_private_key B