How do I define a more stable numbering of proof steps with letters

I have some proofs that require many steps, and I wanted to number them with letters so as to not confuse with the numbers used for Definitions, Axioms, Lemmas and Theorems.

Here is a MWE of what I use – (cfr. question how to enumerate theorems using letters?):

documentclass{article}
usepackage{amsmath, amssymb, amsthm, latexsym}

theoremstyle{plain}
newtheorem{thm}{Theorem}
newtheorem{Ax}[thm]{Axiom}
newtheorem{lem}[thm]{Lemma}

theoremstyle{definition}
newtheorem{df}[thm]{Definition}

newtheoremstyle{exercise}
{topsep}   % above space
{topsep}   % below space
{itshape}  % body font
{0pt}       % indent
{bfseries} % head font
{}         % head punctuation
{5pt plus 1pt minus 1pt} % HEADSPACE
{}          % CUSTOM-HEAD-SPEC

theoremstyle{exercise}

newtheorem{provlinje}{~}
renewcommand*{theprovlinje}{alph{provlinje}}

begin{document}
    
    begin{df}
The words
    end{df}

begin{Ax}
The Assumption
end{Ax}

begin{lem}
An intermediate result
end{lem}
    
begin{thm}
    A Consequence
end{thm}

item{Proof:}
begin{provlinje}
    First line in the proof
end{provlinje}
begin{provlinje}
Second line in the proof
end{provlinje}

begin{df}
More words
end{df}


end{document} ```

The trouble is that this is not a stable solution, and lines soon 
get distorted in the proofs.

How may I improve the definition of 

begin{provlinje}
content
end{provlinje}

to avoid the instability?

**Update**

The problem was resolved, and occurred because I used display math $$Theoremcontent$$, and not just $Theoremcontent$.