Full Idea
Often the purpose of a conditional, 'if p, q', can be served simply by negation and conjunction: not(p and not-q), the so-called 'material conditional'.
Gist of Idea
Some conditionals can be explained just by negation and conjunction: not(p and not-q)
Source
Willard Quine (Philosophy of Logic [1970], Ch.2)
Book Reference
Quine,Willard: 'Philosophy of Logic' [Prentice-Hall 1970], p.24
A Reaction
Logicians love the neatness of that, but get into trouble elsewhere with conditionals, particularly over the implications of not-p.