Definition:Proof

A proof is another name for a valid argument, but in this context the assumption is made that the premises are all true.

That is, a valid argument that has one or more false premises is not a proof.

Suppose $$P$$ is a proposition whose truth or falsehood is to be determined.

Constructing a valid argument upon a set of premises, all of which have previously been established as being true, is called proving $$P$$.