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Transcript
Math 160A - Mathematical Logic - Winter 2016 Quiz #8 — March 7, 2016 NAME: Suppose x is not free in ψ. Prove that the following deduction exists: ∃x(ϕ → ψ) ⊢ ∀xϕ → ψ. By the Deduction Theorem, suffices to show: (1) By Rule EI, it suffices to show i.e., this follows Rule T from the Axiom 2 ------------------------------------------------------------------------Alternate proof: From (1) above, and Contraposition, and the definition of , it suffices to show : By Generalization, since x is not free in This follows by Rule T from the Axiom 2: , it suffices to show: