1) God can be analytically conceived without contradiction.
2) Therefore God is not impossible.
3) By definition God cannot be contingent.
4) Therefore God is either necessary or impossible.
5) God is not impossible (from 2) therefore, God is necessary.

Ax. 1. {P(φ)∧◻∀x[φ(x)→ψ(x)]} →P(ψ)Ax. 2.P(¬φ)↔¬P(φ)Th. 1.P(φ)→◊∃x[φ(x)]Df. 1.G(x)⟺∀φ[P(φ)→φ(x)]Ax. 3.P(G)Th. 2.◊∃xG(x)Df. 2.φ ess x⟺φ(x)∧∀ψ{ψ(x)→◻∀y[φ(y)→ψ(y)]}Ax. 4.P(φ)→◻P(φ)Th. 3.G(x)→G ess xDf. 3.E(x)⟺∀φ[φ ess x→◻∃yφ(y)]Ax. 5.P(E)Th. 4.◻∃xG(x).

You get it, right?

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