Historical prelude. In ancient times, logic was a part of philosophy, not mathematics. It was created and applied by Aristotle and his contemporaries to various geometrical and philosophical problems. With Boole's The Mathematical Analysis of Logic, this changed. Although in many ways anticipated by the work of Leibniz (on what's called the 'algebra of concepts'), Boole's application of algebra to the study of Aristotelian logic made logic a proper part of mathematics. The tools with which mathematicians study logic have since evolved (from algebraic to proof-, model-, category-theoretic, and so on), but the fact remains that logic is now as much a part of mathematics as is set theory.

Fact 1. The language of mathematics is an extension of the language of logic.

1a. Logical vocabulary [math]V_L = \{\lnot, \rightarrow, \forall\}[/math].
1b. Set-theoretic vocabulary [math]V_S = V_L \cup \{\in\}[/math].
1c. Mathematical vocabulary is reducible to [math]V_S[/math].

Fact 2. Logical theorems are also mathematical theorems.

Assuming that by 'logical truths' we understand the classical logical truths and not truths of some deviant or non-classical logic.