Functional predicate: Difference between revisions

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This schema states (in one form), for any functional predicate <i>F</i> in one variable:
: &forall; <i>A</i>, &exist; <i>B</i>, &forall; <i>C</i>, <i>C</i> &isin; <i>A</i> &rarr; <i>F</i>(<i>C</i>) &isin; <i>B</i>.
F irstFirst, we must replace <i>F</i>(<i>C</i>) with some other variable <i>D</i>:
: &forall; <i>A</i>, &exist; <i>B</i>, &forall; <i>C</i>, <i>C</i> &isin; <i>A</i> &rarr; <i>D</i> &isin; <i>B</i>.
Of course, this statment isn't correct; <i>D</i> must be quantified over just after <i>C</i>:
: &forall; <i>A</i>, &exist; <i>B</i>, &forall; <i>C</i>, &forall; <i>D</i>, <i>C</i> &isin; <i>A</i> &rarr; <i>D</i> &isin; <i>B</i>.