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"tax liability does not change" 

Well, the tax DID change, by more than $1,000.  You got an extra $4,050  income (not tax) deduction for the dependent.  That translates to about a $1,000 tax savings if you are in the 25% bracket.  But then the AMT went up.  That's a different tax.

https://turbotax.intuit.com/tax-tools/tax-tips/IRS-Tax-Return/Alternative-Minimum-Tax--Common-Questi...