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\documentclass[12pt,letterpaper]{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{tensor}
\let\oldhat\hat
\renewcommand{\vec}[1]{\mathbf{#1}}
\renewcommand{\hat}[1]{\oldhat{\mathbf{#1}}}
\newcommand{\qvec}[1]{\boldsymbol{#1}}
\begin{document}
Bla bla bla bla :
\begin{align}
\begin{aligned}
\tensor{\qvec{e}}{^0} &= A(z) \, \vec{d}t, \\[8pt]
\tensor{\qvec{e}}{^1} &= B(z) \, \vec{d}x,
\end{aligned}
\intertext{Bla bla bla bla}
\begin{aligned} \nonumber
\vec{d}\tensor{\qvec{e}}{^0} &= A^{\prime} \; \vec{d}z \wedge \vec{d}t, \\[8pt]
\vec{d}\tensor{\qvec{e}}{^1} &= B^{\prime} \; \vec{d}z \wedge \vec{d}x,
\end{aligned}
\end{align}
\end{document}
I could use the
align
environment without the aligned
environment inside, but then how can I number the first two equations as a whole, while leaving the last two equations without any number?