All three of the vaccines in the US are approved.
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They were approved months ago.
First they were approved for human trials. Then, after they had enough data from that, they were approved for emergency use.
You're referring to Pfizer getting approval for standard non-emergency use.
By the way, they didn't skip any steps in the development/testing/approval process. All they did was to perform some steps in parallel that they would normally do in series in order to complete all the steps more quickly.
