Pullback Lemma

Theorem
Let $\mathbf C$ be a metacategory.

Suppose that the following is a commutative diagram in $\mathbf C$:


 * $\begin{xy}\xymatrix@+0.5em{

F \ar[d]_*+{h''} \ar[r]^*+{f'} & E \ar[d]^*+{h'} \ar[r]^*+{g'} & D \ar[d]^*+{h}

\\ A \ar[r]_*+{f} & B \ar[r]_*+{g} & C }\end{xy}$

Suppose furthermore that the right square is a pullback.

Then the left square is a pullback iff the outer rectangle is.