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Syntax Definition wal 1529
Description: Extend wff definition to include the universal quantifier ('for all').  A. x ph is read " ph (phi) is true for all  x." Typically, in its final application  ph would be replaced with a wff containing a (free) occurrence of the variable  x, for example  x  =  y. 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  x. 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  wff  ph
vx  set  x
Assertion
Ref Expression
wal  wff  A. x ph

See definition df-ex 1531 for more information.

Colors of variables: wff set class
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