Combination of two callable swaps - payer & receiver

Hello everyone.

I have some troubles in understanding the non-arbitrage when you hold the following positions:

  • long swap payer vs Libor 1M

  • long cancellable swap receiver vs Libor 1M

  • short cancellable swap payer vs Libor 1M.

Intuitively the total position price (in % p.a.) must be equal to current Libor 1M. But I can not prove it… Does anyone knows the exact rule of how the combination of two opposite callable swaps can be evaluated to be sure the total position is non-arbitrage?

Many thanks in advance!