OD, you are correct! "Be anxious for nothing, ..." is an imperative sentence.
The "mood" is in the imperative which means "a command", "absolutely necessary", "forceful", or "demanding". In other words, it is not a suggestion. In Philippians 4:6 Paul is speaking by divine inspiration, therefore God is saying we have the potential to live anxiety free here on Earth.
Imagine what would happen to the imperative sentence if "for nothing" was left out! We would be left with a command to "be anxious"! Is that the message Paul was meant to deliver? I don't think so!
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