Prove existence of different programs printing each other code

How to prove that there exist two different programs A and B such that A printing code of B and B printing code of A without giving actual examples of such programs?

You maybe know the recursion theorem. It implies, that you can assume that you have a procedure called get_your_own_codeif your programming language is at least as powerful as a Turing machine.

Now do the following

Progr. A
w=get_your_own_code
print "print "+w

Note that some code is hidden in the subroutine of get_you_own_code. So we assume the complete source code is a string called source_code_of_A.

Progr. B
print source_code_of_A

Program A prints:

print source_code_of_A

Program B prints

source_code_of_A

StackExchange Computer Science Q#33685, answer score: 2