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Full Idea
We can construct proofs not out of well-formed formulae ('wffs'), but out of sequents, which are some premises followed by their logical consequence. We explicitly keep track of the assumptions upon which the conclusion depends.
Gist of Idea
We can build proofs just from conclusions, rather than from plain formulae
Source
Theodore Sider (Logic for Philosophy [2010], 2.5.1)
Book Ref
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.39
A Reaction
He says the method of sequents was invented by Gerhard Gentzen (the great nazi logician) in 1935. The typical starting sequents are the introduction and elimination rules. E.J. Lemmon's book, used in this database, is an example.