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Theorem reldmoprab 5932
Description: The domain of an operation class abstraction is a relation. (Contributed by NM, 17-Mar-1995.)
Assertion
Ref Expression
reldmoprab  |-  Rel  dom  {
<. <. x ,  y
>. ,  z >.  | 
ph }
Distinct variable group:    x, y, z
Allowed substitution hints:    ph( x, y, z)

Proof of Theorem reldmoprab
StepHypRef Expression
1 dmoprab 5928 . 2  |-  dom  { <. <. x ,  y
>. ,  z >.  | 
ph }  =  { <. x ,  y >.  |  E. z ph }
21relopabi 4811 1  |-  Rel  dom  {
<. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:   E.wex 1528   dom cdm 4689   Rel wrel 4694   {coprab 5859
This theorem is referenced by:  oprabss  5933  reldmmpt2  5955  tposoprab  6270
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-xp 4695  df-rel 4696  df-dm 4699  df-oprab 5862
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