Resturant depot, a local wholesale food store in US, sells halal meat in bulk which is imported from Australia or New Zealand. The meat is labeled as “Halal” but there is no mention of “Zabiha”.
Almost all local restaurants buy meat from Restaurant Depot.
Is it permissible to use the meat where it is labeled “Halal” but without “Zabiha” label?

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If you can be rest assured that it is coming from a Muslim source and the Muslim source gives the certificate that it is halal you can eat from it. The general rule is that as long as a Muslim informs you it is halal you can take their word. If you have reason to believe that they are untruthful then you should be careful.