Would a Boostmobile SIM card work on an unlocked AT&T or T-Mobile phone?

I hate my current boostmobile phone so bad. I wish I could use it on my old T-Mobile phone, which happens to be unlocked. I know there are certain phones, if unlocked, will allow the SIM card of another wireless phone service provider to work with the unlocked phone. I'm pretty sure AT&T and T-Mobile SIM cards are compatible with one another, once the phones are unlocked. But, will a Boostmobile SIM card work in either one of these phones, if they are unlocked?
 
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