Wdproof12

Proof by Will Dyer

ϕ := ∀y(x = y)

ϕ [y|x] := ∀y(y = y)

This is always true, since y will always equal itself by the axiom y = y.

∃x ϕ = ∃x∀y(x = y)

This is not always true, as there is no singular value of x that can equal every possible value of y.

Ex. Say x = 3, and we iterate through N for values of y. x = y is false for all but one value of N.

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