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Theorem relen 6884
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 6880 . 2  |-  ~~  =  { <. x ,  y
>.  |  E. f 
f : x -1-1-onto-> y }
21relopabi 4827 1  |-  Rel  ~~
Colors of variables: wff set class
Syntax hints:   E.wex 1531   Rel wrel 4710   -1-1-onto->wf1o 5270    ~~ cen 6876
This theorem is referenced by:  bren  6887  isfi  6901  enssdom  6902  ener  6924  sbthcl  6999  xpen  7040  pwen  7050  php3  7063  f1finf1o  7102  isnum2  7594  inffien  7706  cdaen  7815  cdaenun  7816  cdainflem  7833  cdalepw  7838  infmap2  7860  fin4i  7940  fin4en1  7951  isfin4-3  7957  enfin2i  7963  fin45  8034  axcc3  8080  engch  8266  hargch  8315  hasheni  11363  frgpcyg  16543  ctbnfien  27004  enfixsn  27360  mapfien2  27361  lbslcic  27414  en1uniel  27483  pmtrfv  27498
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-opab 4094  df-xp 4711  df-rel 4712  df-en 6880
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