A few points to keep in mind:
1. You would need an iPhone from AT&T (not from Verizon or Sprint).
2. The phone would need to be unlocked!
3. Keep in mind that there are two sizes of SIM cards: mini and micro. iPhone 4 uses the smaller micro SIM. Though there are ways to cut the regular mini SIM to fit in the micro slot.
4. Many features of the iPhone (voice mail for example) require special support from the carrier and may not work properly with other carriers. You might save some money going this route, but be prepared to face a lot of problems and limitations along the way. Not sure if it's worth the trouble. If you do want to switch the carrier, consider getting a smartphone that is supported by that carrier: this would be much cheaper and less troublesome!
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