Full Idea
All demonstrations involve the principle that 'anything implied by a true proposition is true', or 'whatever follows from a true proposition is true'.
Gist of Idea
Demonstration always relies on the rule that anything implied by a truth is true
Source
Bertrand Russell (Problems of Philosophy [1912], Ch. 7)
Book Reference
Russell,Bertrand: 'The Problems of Philosophy' [OUP 1995], p.40
A Reaction
This is modus ponens, a broad principle of rationality, rather than of strict logicality, because it covers practical inferences and vague propositions. Presumably truth is a prior concept to implication, and therefore more metaphysically basic.