⊢(∃x)A≡(∃z)A[x:=z] where z is fresh for A
rules same as here
I proved via hilbert style to prove ⊢(∀x) A ≡ (∀z) A [x:=z] where z is fresh for A but struggling with equational proof for ⊢(∃x)A≡(∃z)A[x:=z] where z is fresh for A
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Maybe you have to use the fact/definition : $(∃x)A \equiv \lnot (∀x) \lnot A$. – Mauro ALLEGRANZA Nov 21 '18 at 08:02
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using that definition, I will get ¬(∀x) ¬A ≡ ¬(∀z) ¬A [x:=z] ? How do you do this equational proof to prove that? – TaeCoda Nov 22 '18 at 17:53