Full Idea
The Principle of Assumptions says that any formula entails itself, i.e. φ |= φ. The principle depends just upon the fact that no interpretation assigns both T and F to the same formula.
Gist of Idea
'Assumptions' says that a formula entails itself (φ|=φ)
Source
David Bostock (Intermediate Logic [1997], 2.5.A)
Book Reference
Bostock,David: 'Intermediate Logic' [OUP 1997], p.30
A Reaction
Thus one can introduce φ |= φ into any proof, and then use it to build more complex sequents needed to attain a particular target formula. Bostock's principle is more general than anything in Lemmon.