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Theorem relen 7541
Description: Equinumerosity is a relation. (Contributed by NM, 28-Mar-1998.)
Assertion
Ref Expression
relen

Proof of Theorem relen
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-en 7537 . 2
21relopabi 5133 1
Colors of variables: wff setvar class
Syntax hints:  E.wex 1612  Relwrel 5009  -1-1-onto->wf1o 5592   cen 7533
This theorem is referenced by:  encv  7544  isfi  7559  enssdom  7560  ener  7582  en1uniel  7607  enfixsn  7646  sbthcl  7659  xpen  7700  pwen  7710  php3  7723  f1finf1o  7766  mapfien2  7888  isnum2  8347  inffien  8465  cdaen  8574  cdaenun  8575  cdainflem  8592  cdalepw  8597  infmap2  8619  fin4i  8699  fin4en1  8710  isfin4-3  8716  enfin2i  8722  fin45  8793  axcc3  8839  engch  9027  hargch  9072  hasheni  12421  pmtrfv  16477  frgpcyg  18612  lbslcic  18876  ctbnfien  30752  mapfien2OLD  31042
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-xp 5010  df-rel 5011  df-en 7537
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