This means "if not" or "unless." It talks about what happens if something does not happen.
Verb [ない-form] + ずはPrimary
This means "if not" or "unless." It talks about what happens if something does not happen.
覚悟せずは、この難局に挑むべきではない。
If one is not prepared, one should not attempt to face this difficult situation.
彼が来ずは、この計画は始まらない。
If he does not come, this plan will not begin.
不断の努力せずは、今日の成功はあり得なかっただろう。
Without constant effort, today's success would likely have been impossible.
知らずは罪だが、知って行わぬは更に大きな罪だ。
Not knowing is a sin, but knowing and not acting is an even greater sin.
君が助けずは、我々は到底この危機を乗り越えられまい。
Unless you help, we will surely be unable to overcome this crisis.
This is like saying 'if not' or 'unless'. It is a very old way to say it. Today, we usually say '～なければ' instead. This form is also like '～ずば'. They mean almost the same thing. The 'は' in '～ずは' can make the 'if not' part feel a bit stronger. Do not confuse it with '～ば' after a verb's 'izenkei' form. That means 'when X happens, Y always happens'.
Watch out: The verbs 'する' (to do) and '来る' (くる - to come) are special. Most verbs change 'ない' to 'ずは'. But 'する' becomes 'せずは'. It does not become 'しずは'. '来る' becomes '来ずは' (こずは).
Don't use this when you are talking to friends. For example, you would not say "友達と会わずは寂しい" (If I don't meet my friends, I'm lonely). This grammar is very old. People do not use it in daily talk. You will see it in old books. You might hear it in old plays. It is for very formal speeches.
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