Reply to "Comment on Sequential Single-pion Production Explaining the dibaryon $d^*(2380)$ peak''

In a comment to our paper on ``Sequential single-pion production explaining the dibaryon $d^*(2380)$ peak'' the authors provide arguments that apparently invalidate our claims and present what they call ``proofs'' of the dibaryon explanation of the $np\to \pi^0\pi^0d$ fusion reaction. In this reply we refute the arguments of the comment and show that no existing experiment proves the dibaryon nature of the peak of the fusion reaction.