If you activate Aggravated Assault during a precombat main phase, after this main phase, you will skip a combat phase and take an additional main phase. Then there will be a combat phase. Then you will have a regularly scheduled postcombat main phase.
The "next combat phase" is indeed one phase.
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Stonehorn Dignitary's ability affects only the next combat phase you would take after the ability resolves. It doesn't say that creatures can't attack during a particular turn or that a player skips all combat phases during their next turn (compare that ability with Orim's Chant and Empty City Ruse [C.R. 108.1]). Assuming Stonehorn Dignitary entered before your turn, if you would otherwise take more than one combat phase during a turn, you will skip only one of them, namely "your next combat phase" after the Stonehorn Dignitary ability resolves (C.R. 614.10, 614.10a).
SD says "skip next combat phase"... and for me next is 1st of those 2 combat phases.
The "next combat phase" is indeed one phase.
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