Quantifier shift

A logical fallacy in which the quantifiers of a statement are erroneously transposed.

Definition

For every A, there is a B, such that C. Therefore, there is a B, such that for every A, C.

$\forall$x $\exists$y(Rxy) therefore $\exists$y$\forall$x(Rxy)
OR

There is an A, such that for every B, C. Therefore, for every B, there is an A, such that C.

$\exists$y$\forall$x(Rxy) therefore $\forall$x $\exists$y(Rxy)

Examples

Every person has a woman that is their mother. Therefore, there is a woman that is the mother of every person.

$\forall$x$\exists$y((Px $\to$ Wy & M(yx)

Everybody has something to believe in. Therefore, there is something that everybody believes in.