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

Theorem reldom 7044
Description: Dominance is a relation. (Contributed by NM, 28-Mar-1998.)
Assertion
Ref Expression
reldom  |-  Rel  ~<_

Proof of Theorem reldom
Dummy variables  x  y  f are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-dom 7040 . 2  |-  ~<_  =  { <. x ,  y >.  |  E. f  f : x -1-1-> y }
21relopabi 4933 1  |-  Rel  ~<_
Colors of variables: wff set class
Syntax hints:   E.wex 1547   Rel wrel 4816   -1-1->wf1 5384    ~<_ cdom 7036
This theorem is referenced by:  relsdom  7045  brdomg  7047  brdomi  7048  domtr  7089  undom  7125  xpdom2  7132  xpdom1g  7134  domunsncan  7137  sbth  7156  sbthcl  7158  dom0  7164  fodomr  7187  pwdom  7188  domssex  7197  mapdom1  7201  mapdom2  7207  fineqv  7253  infsdomnn  7297  infn0  7298  elharval  7457  harword  7459  domwdom  7468  unxpwdom  7483  infdifsn  7537  infdiffi  7538  ac10ct  7841  iunfictbso  7921  cdadom1  7992  cdainf  7998  infcda1  7999  pwcdaidm  8001  cdalepw  8002  unctb  8011  infcdaabs  8012  infunabs  8013  infpss  8023  infmap2  8024  fictb  8051  infpssALT  8119  fin34  8196  ttukeylem1  8315  fodomb  8330  wdomac  8331  brdom3  8332  iundom2g  8341  iundom  8343  infxpidm  8363  iunctb  8375  gchdomtri  8430  pwfseq  8465  pwxpndom2  8466  pwxpndom  8467  pwcdandom  8468  gchaclem  8471  gchpwdom  8475  reexALT  10531  hashdomi  11574  cctop  16986  1stcrestlem  17429  2ndcdisj2  17434  dis2ndc  17437  hauspwdom  17478  ufilen  17876  ovoliunnul  19263  uniiccdif  19330  ovoliunnfl  25946  voliunnfl  25948  volsupnfl  25949
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361  ax-sep 4264  ax-nul 4272  ax-pr 4337
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ne 2545  df-ral 2647  df-rex 2648  df-rab 2651  df-v 2894  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-if 3676  df-sn 3756  df-pr 3757  df-op 3759  df-opab 4201  df-xp 4817  df-rel 4818  df-dom 7040
  Copyright terms: Public domain W3C validator