The "plain" old Sierra, Speer, and Hornady soft point killed tons of elk before all copper, super bonded ballistic testicled magnasonic triple hollow tungsten core bullets were even thought of. So yeah they'll be fine. Like Dan says, shoot them where you're supposed to and you'll have no worries.
Of course if you want to shoot one like they're not supposed to show on TV you'd be better off with a tougher bullet for the insurance.
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