Download By Rule EI, it suffices to show -------------------------------------------------------

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: