Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  relen Structured version   Unicode version

Theorem relen 7116
 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 7112 . 2
21relopabi 5002 1
 Colors of variables: wff set class Syntax hints:  wex 1551   wrel 4885  wf1o 5455   cen 7108 This theorem is referenced by:  bren  7119  isfi  7133  enssdom  7134  ener  7156  sbthcl  7231  xpen  7272  pwen  7282  php3  7295  f1finf1o  7337  isnum2  7834  inffien  7946  cdaen  8055  cdaenun  8056  cdainflem  8073  cdalepw  8078  infmap2  8100  fin4i  8180  fin4en1  8191  isfin4-3  8197  enfin2i  8203  fin45  8274  axcc3  8320  engch  8505  hargch  8554  hasheni  11634  frgpcyg  16856  ctbnfien  26881  enfixsn  27236  mapfien2  27237  lbslcic  27290  en1uniel  27359  pmtrfv  27374 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-opab 4269  df-xp 4886  df-rel 4887  df-en 7112
 Copyright terms: Public domain W3C validator