Full Idea
The Principle of Cutting is the general point that entailment is transitive, extending this to cover entailments with more than one premiss. Thus if γ |= φ and φ,Δ |= ψ then γ,Δ |= ψ. Here φ has been 'cut out'.
Gist of Idea
'Cutting' allows that if x is proved, and adding y then proves z, you can go straight to z
Source
David Bostock (Intermediate Logic [1997], 2.5.C)
Book Reference
Bostock,David: 'Intermediate Logic' [OUP 1997], p.31
A Reaction
It might be called the Principle of Shortcutting, since you can get straight to the last conclusion, eliminating the intermediate step.