5.121 The truth-grounds of q are contained in those of p; p follows from q.
5.122 If p follows from q, the sense of "p" is contained in that of "q".
5.123 If a god creates a world in which certain propositions are true, he creates thereby also a world in which all propositions consequent on them are true. And similarly he could not create a world in which the proposition "p" is true without creating all its objects.
5.124 A proposition asserts every proposition which follows from it.
5.1241 "p.q" is one of the propositions which assert "p" and at the same time one of the propositions which assert "q".
Two propositions are opposed to one another if there is no significant proposition which asserts them both.
Every proposition which contradicts another, denies it.
5.13 That the truth of one proposition follows from the truth of other propositions, we perceive from the structure of the propositions.
5.131 If the truth of one proposition follows from the truth of others, this expresses itself in relations in which the forms of these propositions stand to one another, and we do not need to put them in these relations first by connecting them with one another in a proposition; for these relations are internal, and exist as soon as, and by the very fact that, the propositions exist.
5.1311 When we conclude from pvq and ~p to q the relation between the forms of the propositions "pvq" and "~p" is here concealed by the method of symbolizing. But if we write, e.g. instead of "pvq" "p|q .|. p|q" and instead of "~p" "p|p" (p|q = neither p nor q), then the inner connexion becomes obvious.