Saturday, January 07, 2012
Proof Ex 3.28
Given
∀y∃z∀xP(x,y,z)
Prove that
∀x∀y∃zP(x,y,z)
Proof:
Let a,b be arbitrary
We need to show ∃zP(a,b,z)
Given ∀y∃z∀xP(x,y,z), it follows ∃z∀xP(x,b,z)
Let c be such that ∀xP(x,b,c)
So P(a,b,c)
Thus ∀x∀y∃zP(x,y,z)
