Center align equations and left align implication arrows

Question

I'm trying to align multiple equations within a proof, and use implication arrows to denote next steps.

I want the equations to be centered like how normal align would, but I want the implication arrows to be left aligned as well.

I imagine the arrows looking like \tag*{$\implies$} but on the left-hand side.

I've tried different manipulations of the align environment, but can't achieve what I'm looking for.

\begin{align*}
    a &= b \\
    \implies 2a &= 2b \\
    \implies f(2a) &= f(2b) \\
\end{align*}

\begin{align*}
    && a &= b \\
    \implies&& 2a &= 2b \\
    \implies&& f(2a) &= f(2b) \\
\end{align*}

\begin{align*}
    & a &&= b \\
    \implies& 2a &&= 2b \\
    \implies& f(2a) &&= f(2b) \\
\end{align*}

Answer 1

Like this?

(red liens indicate text area borders)

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{alignat*}{3}
&               &\quad       a & = b \\
&   \implies    &\quad      2a & = 2b \\
&   \implies    &\quad   f(2a) & = f(2b)
\end{alignat*}
\end{document}

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{flalign*}
&               &       a & = b     &   \\
&   \implies    &      2a & = 2b    &   \\
&   \implies    &   f(2a) & = f(2b) &
\end{flalign*}
\end{document}

Edit: or you looking for the following:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{flalign*}
&               &       a & = b     &   \\
&   \implies    &      2a & = 2b    &   \\
&   \implies    &   f(2a) & = f(2b) &
\end{flalign*}
\end{document}