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The article introduces propositional linear time temporal logic as a formal system. Axioms and rules of derivation are defined. Soundness Theorem and Deduction Theorem are proved [9].Institute of Sociology, University of Białystok, PolandGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55- 65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Adam Grabowski. Hilbert positive propositional calculus. Formalized Mathematics, 8(1):69-72, 1999.Fred Kröger and Stephan Merz. Temporal Logic and State Systems. Springer-Verlag, 2008.Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.Andrzej Trybulec. Defining by structural induction in the positive propositional language. Formalized Mathematics, 8(1):133-137, 1999.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Many-argument relations. Formalized Mathematics, 1(4):733-737, 1990

The Axiomatization of Propositional Linear Time Temporal Logic