The idea is to proof validity of
∃x(Fx ^ Gx) / ∃xFx
To do this I understand you assume invalid and get a contradiction. I have the answer but I don't understand the wording
∃x(Fx ^ Gx) is true-in-I, which means some object o∈D satisfies Fx ^ Gx, which means o is such that both o∈ext(F) and o∈ext(G).
∃xFx is false-in-I, which means every object o
∈D is such that o∉ext(F).
Since what holds of o` holds of everything in the domain of I, and since o∉D, o∉ext(F). Contradiction, so there is no such interpretation. Thus valid.
what I don't get is the last statement "since what holds of o' holds of everything in the domain of I" how does that go to "since o∉D" when we are talking about o' and not o and we had established o is contained in D already (I get we need the contradiction, but from where was this generated?)