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For example if we take Faraday's law:

Curl(E)-dB/dt=0

And I take the curl of both sides:

Curl(Curl(E))-Curl(dB/dt)=0

Is

Curl(dB/dt)=d/dt(Curl(B))

I assume this is only true for a certain condition but I can't think of anything?

If you have some insight please let me know