# A quick question about a logical negation

I just want to make sure I'm negating the following logical statement correctly (for a contradiction proof):

For every set $A$, there exists a well ordered set $V$ such that there exists no surjection $\pi: A \rightarrow V$.

I'm negating this as:

For every set $A$, there exists a well ordered set $V$ such that there exists a surjection $\pi: A \rightarrow V$.

Is this a correct negation?

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There exists a set $A$ so that for all well-ordered sets $V$ there exists a surjection $\pi:A\to V$.