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Syntax Definition wal 1240
Description: Extend wff definition to include the universal quantifier ('for all'). is read " (phi) is true for all ." Typically, in its final application would be replaced with a wff containing a (free) occurrence of the variable , for example . In a universe with a finite number of objects, "for all" is equivalent to a big conjunction (AND) with one wff for each possible case of . When the universe is infinite (as with set theory), such a propositional-calculus equivalent is not possible because an infinitely long formula has no meaning, but conceptually the idea is the same.
Ref Expression
vx.wal  setvar
Ref Expression

See definition df-tru 1245 for more information.

Colors of variables: wff set class
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