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Theorem mathbox 10847
Description: (This theorem is a dummy placeholder for these guidelines. The name of this theorem, "mathbox", is hard-coded into the Metamath program to identify the start of the mathbox section for web page generation.)

A "mathbox" is a user-contributed section that is maintained by its contributor independently from the main part of

For contributors:

By making a contribution, you agree to release it into the public domain, according to the statement at the beginning of

Mathboxes are provided to help keep your work synchronized with changes in, but they shouldn't be depended on as a permanent archive. If you want to preserve your original contribution, it is your responsibility to keep your own copy of it along with the version of that works with it.


1. If at all possible, please use only nullary class constants for new definitions.

2. Try to follow the style of the rest of Each $p and $a statement must be immediately preceded with the comment that will be shown on its web page description. The metamath program command "write source /rewrap" will take care of wrapping comment lines and indentation conventions. All mathbox content will be on public display and should hopefully reflect the overall quality of the website.

3. Before submitting a revised mathbox, please make sure it verifies against the current

4. Mathboxes should be independent i.e. the proofs should verify with all other mathboxes removed. If you need a theorem from another mathbox, that is fine (and encouraged), but let me know, so I can move the theorem to the main section. One way avoid undesired accidental use of other mathbox theorems is to develop your mathbox using a modified that has mathboxes removed.


1. We may decide to move some theorems to the main part of for general use.

2. We may make changes to mathboxes to maintain the overall quality of Normally we will let you know if a change might impact what you are working on.

3. If you use theorems from another user's mathbox, we don't provide assurance that they are based on correct or consistent $a statements. (If you find such a problem, please let us know so it can be corrected.) (Contributed by NM, 20-Feb-2007.) (New usage is discouraged.)

Ref Expression
mathobox.1  |-  ph
Ref Expression
mathbox  |-  ph

Proof of Theorem mathbox
StepHypRef Expression
1 mathobox.1 1  |-  ph
Colors of variables: wff set class
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator