+---+---+---+---+ | a | b | c | d | A +---+---+---+---+ | e | f | g | h | B +---+---+---+---+ | i | j | k | l | C +---+---+---+---+ D E F GThe number abcd is denoted by A, that is, A = 1000a + 100b + 10c + d, and the same for the other 2 horizontal numbers B and C.

The number aei is denoted by D, that is, D = 100a + 10e + i, and the same for the other 3 vertical numbers E, F and G.

Prove that if any 6 of these numbers (A, B, C, D, E, F, G) are divisible by 7, then the last number must also be divisible by 7.