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Theorem relen 6291
Description: Equinumerosity is a relation. (Contributed by NM, 28-Mar-1998.)
Assertion
Ref Expression
relen  |-  Rel  ~~

Proof of Theorem relen
Dummy variables  x  y  f are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-en 6288 . 2  |-  ~~  =  { <. x ,  y
>.  |  E. f 
f : x -1-1-onto-> y }
21relopabi 4491 1  |-  Rel  ~~
Colors of variables: wff set class
Syntax hints:   E.wex 1422   Rel wrel 4376   -1-1-onto->wf1o 4931    ~~ cen 6285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-opab 3848  df-xp 4377  df-rel 4378  df-en 6288
This theorem is referenced by:  encv  6293  isfi  6308  enssdom  6309  ener  6326  en1uniel  6351  xpen  6386
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