You have tagged this query with both cite-package and biblatex. Unfortunately for you, the cite and biblatex packages are mutually incompatible.
To use the cite package, you must also (a) provide a suitable \bibliographystyle instruction and (b) run BibTeX. To use the biblatex package, you must (i) not load the cite package, (ii) use biber rather than BibTeX, and (iii) replace the single instruction \bibliography{bibliography.bib} with two instructions: insert \addbibresource{bibliography.bib} in the preamble (after loading the biblatex package), and insert \printbibliography in the document in the location where the formatted bibliography is supposed to be inserted.
I'm not aware of the existence of a ready-made biblatex style called prop. Given your comment that you were "advised to use \bibliographystyle{prop} and \bibliography{<databasefilename>}, [a]nd then to run through bibtex," I will assume that you really do need to use the cite package with BibTeX as the back-end, rather than the biblatex package with the biber back-end.
If the good folks who provide the LaTeX document class file prop2015.cls also provide a bibliography style file called prop.bst, and if the raw bibliographic entries are contained in a file called bibliography.bib, you should thus proceed as follows.
First, reorganize your document so that its structure resembles the following layout:
\documentclass{prop2015}
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage{graphicx}
%%\usepackage[english]{babel} % Don't load packages more than once
\usepackage{amsmath}
%%\usepackage{amsfonts} % Is loaded automatically by 'amssymb'
\usepackage{amssymb}
\usepackage{breqn}
\usepackage{cite} % the package called "cite"
\bibliographystyle{prop}
\usepackage{hyperref} % this package must be loaded _last_
\begin{document}
%% ... various \cite instructions ...
\bibliography{bibliography} % don't use the ".bib" extension here
\end{document}
(Aside: Do please make a habit of not trying to load packages more than once.)
Second, once the document compiles without syntax errors, be sure to run LaTeX, BibTeX, and LaTeX twice more on the main tex file. Doing so will create (a) the formatted bibliography and (b) the numeric-style citation call-outs to the bib entries in the body of the document.
\bibliographystylepresupposes the use of BibTeX, to create the formatted bibliography. However, you seem to also want to use thebiblatexpackage with thebiberbackend, not BibTeX. For sure, theciteandbiblatexpackages are mutually incompatible. Which method are you supposed to be using -- BibTeX or biber? Please advise. – Mico Feb 03 '19 at 19:34\bibliographystyle{prop}and\bibliography{<databasefilename>}. And then to run through bibtex. – madmiKe Feb 03 '19 at 19:41biblatexpackage at all. Instead, be sure to run latex, then bibtex, and finally latex twice more to generate (a) the formatted bibliography and (b) the in-text citation call-outs. – Mico Feb 03 '19 at 19:51Missing 'biblatex' package.– madmiKe Feb 03 '19 at 20:06.auxfile and allow a new non-biblatex one to be generated. – David Carlisle Feb 03 '19 at 20:29citeornatbib) and are strictly incompatible withbiblatex. Publisher.bstfiles can't be used withbiblatex, either (style=propshould fail unless you have abiblatexstyle called prop residing inprop.bbxandprop.cbx). Removebiblatexand all of its commands and then delete the temporary files (.aux,.bbl,.bcf) and recompile. – moewe Feb 04 '19 at 08:59