Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989 Association of Mizar Users

## Connectives and Subformulae of the First Order Language

Grzegorz Bancerek
Warsaw University, Bialystok
Partially supported by RPBP.III-24.C1.

### Summary.

In the article the development of the first order language defined in [4] is continued. The following connectives are introduced: implication (\$\Rightarrow\$), disjunction (\$\vee\$), and equivalence (\$\Leftrightarrow\$). We introduce also the existential quantifier (\$\exists\$) and FALSUM. Some theorems on disjunctive, conditional, biconditional and existential formulae are proved and their selector functors are introduced. The second part of the article deals with notions of subformula, proper subformula and immediate constituent of a QC-formula.

#### MML Identifier: QC_LANG2

The terminology and notation used in this paper have been introduced in the following articles [6] [5] [8] [9] [3] [1] [2] [7] [4]

Contents (PDF format)

#### Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[4] Piotr Rudnicki and Andrzej Trybulec. A first order language. Journal of Formalized Mathematics, 1, 1989.
[5] Andrzej Trybulec. Enumerated sets. Journal of Formalized Mathematics, 1, 1989.
[6] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[7] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[8] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[9] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.