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Theorem resdm 5320
Description: A relation restricted to its domain equals itself. (Contributed by NM, 12-Dec-2006.)
Assertion
Ref Expression
resdm

Proof of Theorem resdm
StepHypRef Expression
1 ssid 3522 . 2
2 relssres 5316 . 2
31, 2mpan2 671 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  C_wss 3475  domcdm 5004  |`cres 5006  Relwrel 5009
This theorem is referenced by:  resindm  5323  resdm2  5502  relresfld  5539  relcoi1  5541  fnex  6139  dftpos2  6991  tfrlem11  7076  tfrlem15  7080  tfrlem16  7081  pmresg  7466  domss2  7696  axdc3lem4  8854  gruima  9201  funsseq  29199  seff  31189  sblpnf  31190  resisresindm  32305  bnj1321  34083
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-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-dm 5014  df-res 5016
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