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Theorem relen 6638
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 6635 . 2  |-  ~~  =  { <. x ,  y
>.  |  E. f 
f : x -1-1-onto-> y }
21relopabi 4665 1  |-  Rel  ~~
Colors of variables: wff set class
Syntax hints:   E.wex 1468   Rel wrel 4544   -1-1-onto->wf1o 5122    ~~ cen 6632
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-opab 3990  df-xp 4545  df-rel 4546  df-en 6635
This theorem is referenced by:  encv  6640  isfi  6655  enssdom  6656  ener  6673  en1uniel  6698  xpen  6739  enomnilem  7010  djuenun  7073  cc3  7088  pwf1oexmid  13278
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