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Theorem resdm2 5352
 Description: A class restricted to its domain equals its double converse. (Contributed by NM, 8-Apr-2007.)
Assertion
Ref Expression
resdm2

Proof of Theorem resdm2
StepHypRef Expression
1 rescnvcnv 5324 . 2
2 relcnv 5234 . . 3
3 resdm 5176 . . 3
42, 3ax-mp 8 . 2
5 dmcnvcnv 5084 . . 3
65reseq2i 5135 . 2
71, 4, 63eqtr3ri 2464 1
 Colors of variables: wff set class Syntax hints:   wceq 1652  ccnv 4869   cdm 4870   cres 4872   wrel 4875 This theorem is referenced by:  resdmres  5353  fimacnvinrn  24039 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-xp 4876  df-rel 4877  df-cnv 4878  df-dm 4880  df-rn 4881  df-res 4882
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