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Syntax Definition wal 1393
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.
Hypotheses
Ref Expression
wph
vx.wal No typesetting for: setvar x
Assertion
Ref Expression
wal No typesetting for: wff A. x ph

See definition df-tru 1398 for more information.

Colors of variables: wff setvar class
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