$\rho$-assoc and $\rho$-dist of wfs and f in $\Sigma$ and $\mathscr{L_{HA}}$-theory on 0-OL

Abstract

In this paper we create pseudo associativity ($\rho$-assoc) and pseudo distributivity ($\rho$-dist) properties for not fundamental operators NFO $\downarrow$, $\uparrow$, using two semantic rules, also we build proofs for this result in Hilbert-Ackermann ($\mathscr{HA}$) axiomatic system, all in the 0-order logic (0-OL) context.