Implicative normal form

A propositional form of the type

$$C_1\supset(C_2\supset\ldots(C_n\supset\bot)\ldots),$$

where all the $C_i$, $i=1,\ldots,n$, have the form

$$C_{i1}\supset(C_{i2}\supset\ldots(C_{im_i}\supset\bot)\ldots).$$

Here, each $C_{ij}$ ($i=1,\ldots,m$; $j=1,\ldots,m_i$) is either a variable or the negation of a variable, and $\bot$ is the logical symbol denoting falsehood. For each propositional formula $A$ one can construct an implicative normal form $B$ classically equivalent to it and containing the same variables as $A$. Such a $B$ is called an implicative normal form of $A$.

References

[1]	A. Church, "Introduction to mathematical logic" , 1 , Princeton Univ. Press (1956)