This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem relen

Description: Equinumerosity is a relation. (Contributed by NM, 28-Mar-1998)

Ref Expression
Assertion relen 
|- Rel ~~

Proof

Step Hyp Ref Expression
1 df-en 
 |-  ~~ = { <. x , y >. | E. f f : x -1-1-onto-> y }
2 1 relopabiv 
 |-  Rel ~~