# What is the definition of parity conservation?

I searched quite hard, and am still confused what is the exact definition of parity conservation? For example, we have quantum system with initial state $\Phi_i$, and after decaying it comes to final state $\Phi_f$. The energy conservation means $E_i = E_f$, where $E_i$ and $E_f$ are energies of initial and final states, respectively. This "energy conservation" is quite easy to understand. Similarly, I was expecting a definition of "parity conservation" as something like (hereafter I call definition 1) $\pi_i = \pi_f$ where $\pi_i$ and $\pi_f$ are the parities of initial and final states, respectively. But I googled quite a lot, and most answers are something like (hereafter call definition 2): "Parity conservation means the mirror image and the original systems must behave identically". I know what definition 2 means, but I don't know why parity conservation means that. Are "definition 1" and "definition 2" identical? Can "definition 1" be derived from "definition 2" or vice verse can "definition 2" be derived from "definition 1" ? I searched there is one similar question but I don't understand the answer -:(( Can someone explain with somewhat plain words?

Edit: Because parity corresponds to the symmetry group $\mathbb{Z}_2$, if you properly assign intrinsic parities to particles, then you can show that def #2 implies that parity is "conserved" in the modified sense that the "product" of parities for incoming particles and outgoing particles should be equal if parity is a symmetry of the interaction, up to overall parity configuration of the products.