DEDUCIBILITY THEOREMS IN MATHEMATICS LOGIC


These theorems, due to Smarandache, are defined in the Propositional 
Calculus of Mathematics Logic as:
                   ___
  If     I---   A  ___I B ,  for i = 1, 2, ..., n,  then:
                 i       i
                                      ___
     a)  I---   A  /\ A  /\ ... /\ A  ___I B  /\ B  /\ ... /\ B ;             
                 1     2            n       1     2            n
                                      ___
     a)  I---   A  \/ A  \/ ... \/ A  ___I B  \/ B  \/ ... \/ B .             
                 1     2            n       1     2            n


Reference:
  Smarandache, F., "Deducibility theorems in mathematics logics", in 
    <An. Univ. Timisoara>, seria St. Matematice, Vol. XVII, fasc. 2,  
    163-168, 1979.