# Subordinate Proof (Subproof)

In a subproof, we start by choosing a formula that we assume is true within the subproof. Then we see what we can prove based on that assumption and any previously deduced formulas.

- Conditional proof (imp_i)
- Indirect proof/proof by contradiction (raa)
- Case analysis (cases)

General form of subproof: x) sub proof opening R { $⋮$ x+y) Q by rule B } x+y+1) P by rule C on x – x+y