A statement about theorems. It usually gives a criterion for getting a new theorem from an old one, either by changing its objects according to a rule (duality principle), or by transferring it to another area (from the theory of categories to the theory of groups) or to another context within the same area (from linear transformations to matrices).

# Metatheorem

## See also

Metamathematics, Metatheory, Theorem
*This entry contributed by Margherita
Barile*

## Explore with Wolfram|Alpha

## References

Mitchell, B. "Metatheorems." §4.1 in*Theory of Categories.*New York: Academic Press, pp. 93-97, 1965.Winter, D. J.

*Matrix Algebra.*New York: MacMillan, p. 295, 1992.

## Referenced on Wolfram|Alpha

Metatheorem## Cite this as:

Barile, Margherita. "Metatheorem." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/Metatheorem.html