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 #1
Mathelogician
Member
 Aug 6, 2012
 35
Hi everybody!
I am confused about what is the role of the condition " xdoesn't belong to FV(phi)" in theorems like (i),(ii) or similarly in (iii) and (iv) .
I know that the philosophy of the condition "the variable z's being free for x in phi" is to avoid the phenomenon that a free variable turn to be bound after aubstituation. But i certainly don't get the point of the first type conditions!
==========================================
Any help would be thanked; the more precise one, the deeper one!!
Note: FV(phi):= the set of free variables of phi ; and i am using Van Dalen's Logic and structure.
I am confused about what is the role of the condition " xdoesn't belong to FV(phi)" in theorems like (i),(ii) or similarly in (iii) and (iv) .
I know that the philosophy of the condition "the variable z's being free for x in phi" is to avoid the phenomenon that a free variable turn to be bound after aubstituation. But i certainly don't get the point of the first type conditions!
==========================================
Any help would be thanked; the more precise one, the deeper one!!
Note: FV(phi):= the set of free variables of phi ; and i am using Van Dalen's Logic and structure.
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