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Theorem relen 7320
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 7316 . 2  |-  ~~  =  { <. x ,  y
>.  |  E. f 
f : x -1-1-onto-> y }
21relopabi 4970 1  |-  Rel  ~~
Colors of variables: wff setvar class
Syntax hints:   E.wex 1586   Rel wrel 4850   -1-1-onto->wf1o 5422    ~~ cen 7312
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-9 1760  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423  ax-sep 4418  ax-nul 4426  ax-pr 4536
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2573  df-ne 2613  df-ral 2725  df-rex 2726  df-rab 2729  df-v 2979  df-dif 3336  df-un 3338  df-in 3340  df-ss 3347  df-nul 3643  df-if 3797  df-sn 3883  df-pr 3885  df-op 3889  df-opab 4356  df-xp 4851  df-rel 4852  df-en 7316
This theorem is referenced by:  encv  7323  bren  7324  isfi  7338  enssdom  7339  ener  7361  en1uniel  7386  enfixsn  7425  sbthcl  7438  xpen  7479  pwen  7489  php3  7502  f1finf1o  7544  mapfien2  7663  isnum2  8120  inffien  8238  cdaen  8347  cdaenun  8348  cdainflem  8365  cdalepw  8370  infmap2  8392  fin4i  8472  fin4en1  8483  isfin4-3  8489  enfin2i  8495  fin45  8566  axcc3  8612  engch  8800  hargch  8845  hasheni  12124  pmtrfv  15963  frgpcyg  18011  lbslcic  18275  ctbnfien  29162  mapfien2OLD  29454
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