Универсальная теорема дедукции.

Abstract

The main aim of the paper is to formulate the deduction theorem which would be valid for any logical theory T closed by MP.

The using of MP in a consequence $B_l,...B_m$ of inference В from hypotheses $\varGamma$ in a theory $T$ is said to be normalized ifffor each member of the consequence $B_i$ $(i\leq m)$, obtained from $B_k$ and $B_l$ $(k,l\leq i)$ by $MP$, the following conditions are satisfied: $(a)$ if $B_k$ is the major premise of $MP$ and has a form $B_l\rightarrow B_i$, then it precedes the minor one $B_l$, $(b)$ there is no any member $B_k$ $(l\geq k\geq i)$ of the consequence between Bj and B, except members which are result of $MP$ with the same minor premise $B_l$; $(c)$ $B_l$ doesn’t depend from any hypotheses preceding the major premise $B_k$.