Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990 Association of Mizar Users

## A First-Order Predicate Calculus

Agata Darmochwal
Warsaw University, Bialystok
Supported by RPBP.III-24.C1.

### Summary.

A continuation of [7], with an axiom system of first-order predicate theory. The consequence Cn of a set of formulas $X$ is defined as the intersection of all theories containing $X$ and some basic properties of it has been proved (monotonicity, idempotency, completeness etc.). The notion of a proof of given formula is also introduced and it is shown that ${\rm Cn} X = \{~p: p$ has a proof w.r.t. $X\}$. First 14 theorems are rather simple facts. I just wanted them to be included in the data base.

#### MML Identifier: CQC_THE1

The terminology and notation used in this paper have been introduced in the following articles [10] [6] [12] [2] [13] [5] [3] [1] [8] [4] [11] [9] [7]

Contents (PDF format)

#### Bibliography

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[3] Grzegorz Bancerek. Sequences of ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
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[6] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
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[8] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
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[13] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.