\documentclass{article}

\usepackage{amsmath}
%proof environment
\usepackage{amsthm}

\newtheorem{Axiom}{Axioma}
\newtheorem{Theorem}{Teorema}[section]

\newtheorem
    {Definition}
    [Theorem]
    {Defini\c{c}\~ao}
\newtheorem
    {Proposition}
    [Theorem]
    {Proposi\c{c}\~o}
\newtheorem
    {Corollary}
    [Theorem]
    {Corol\'ario}
\newtheorem
    {Lemma}
    [Theorem]
    {Lema}

\newtheorem
    {Comment}
    [Theorem]
    {Comment}
    

\begin{document}

\section{Hello World}

   \begin{Theorem}
       My first theorem...
   \end{Theorem}
   \begin{Definition}
       My first theorem...
   \end{Definition}
   \begin{Theorem}
       My second theorem...
   \end{Theorem}

   \begin{proof}
      Here's the proof...
   \end{proof}

\end{document}
