This means you do something without another thing. Or, something exists but is missing another thing. It is a formal way to say 'without X'.
Noun + なしにPrimary
Verb [dictionary form] + こと + なしに
This means you do something without another thing. Or, something exists but is missing another thing. It is a formal way to say 'without X'.
予告なしに、抜き打ちテストが実施された。
A surprise test was conducted without any prior notice.
涙なしには、この映画のラストシーンは見られない。
You can't watch the last scene of this movie without tears.
彼は誰にも相談することなしに、会社を辞めてしまった。
He quit the company without consulting anyone.
皆様のご協力なしに、このプロジェクトの成功はあり得ませんでした。
The success of this project would not have been possible without everyone's cooperation.
明確な目標なしに努力を続けても、大きな成果は期待できない。
Even if you continue to put in effort without a clear goal, you can't expect great results.
This grammar shows that something is very important. It's like saying, 'You really need this thing.' Without it, something else cannot happen. The 'は' makes the 'without' part stand out a lot.
This is more formal than 〜ないで. It means something important was missing. 〜ないで just says you did not do something. This is also more formal than 〜ず. But it is not as old-fashioned as 〜ずして.
Don't use this when you just mean "without doing something." For example, "I went out without an umbrella" is better with 〜ないで.
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