Yes, player A still gets whatever the artifact taps to do to happen. The ability of Treasure Nabber will go on the stack in response to the artifact being tapped but the artifact's tap ability will also be on the stack and resolve as normal. In this case they will get the 2 mana.
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I have officially moved to MTGNexus. I just wanted to let people know as my response time to salvation decks being bumped is very hit or miss.
Player A: taps sol ring for mana
Player B: gets control of sol ring tapped with treasure nabber
Does player A still get the mana from sol ring on that turn before it switches control or does player B get the mana on that same turn
Or neither?
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[Modern] Allies