J.R. S. answered 04/12/18
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Ph.D. in Biochemistry--University Professor--Chemistry Tutor
As pointed out by Arturo, the hydronium (H3O+) forms by the autoionization of water molecules, but you are also correct. When an acid is dissolved in water, you also get the formation of additional hydronium ions.
H2O + H+ <==> H3O+