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Theorem relen 7521
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 7517 . 2  |-  ~~  =  { <. x ,  y
>.  |  E. f 
f : x -1-1-onto-> y }
21relopabi 5128 1  |-  Rel  ~~
Colors of variables: wff setvar class
Syntax hints:   E.wex 1596   Rel wrel 5004   -1-1-onto->wf1o 5587    ~~ cen 7513
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-opab 4506  df-xp 5005  df-rel 5006  df-en 7517
This theorem is referenced by:  encv  7524  bren  7525  isfi  7539  enssdom  7540  ener  7562  en1uniel  7587  enfixsn  7626  sbthcl  7639  xpen  7680  pwen  7690  php3  7703  f1finf1o  7746  mapfien2  7868  isnum2  8326  inffien  8444  cdaen  8553  cdaenun  8554  cdainflem  8571  cdalepw  8576  infmap2  8598  fin4i  8678  fin4en1  8689  isfin4-3  8695  enfin2i  8701  fin45  8772  axcc3  8818  engch  9006  hargch  9051  hasheni  12389  pmtrfv  16283  frgpcyg  18407  lbslcic  18671  ctbnfien  30384  mapfien2OLD  30674
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