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Theorem dmoprab 5616
 Description: The domain of an operation class abstraction. (Contributed by NM, 17-Mar-1995.) (Revised by David Abernethy, 19-Jun-2012.)
Assertion
Ref Expression
dmoprab
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem dmoprab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfoprab2 5583 . . 3
21dmeqi 4564 . 2
3 dmopab 4574 . 2
4 exrot3 1621 . . . . 5
5 19.42v 1828 . . . . . 6
652exbii 1538 . . . . 5
74, 6bitri 182 . . . 4
87abbii 2195 . . 3
9 df-opab 3848 . . 3
108, 9eqtr4i 2105 . 2
112, 3, 103eqtri 2106 1
 Colors of variables: wff set class Syntax hints:   wa 102   wceq 1285  wex 1422  cab 2068  cop 3409  copab 3846   cdm 4371  coprab 5544 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-dm 4381  df-oprab 5547 This theorem is referenced by:  dmoprabss  5617  reldmoprab  5620  fnoprabg  5633  dmaddpq  6631  dmmulpq  6632
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