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Theorem dmoprab 6146
 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 6113 . . 3
21dmeqi 5063 . 2
3 dmopab 5072 . 2
4 exrot3 1759 . . . . 5
5 19.42v 1928 . . . . . 6
652exbii 1593 . . . . 5
74, 6bitri 241 . . . 4
87abbii 2547 . . 3
9 df-opab 4259 . . 3
108, 9eqtr4i 2458 . 2
112, 3, 103eqtri 2459 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550   wceq 1652  cab 2421  cop 3809  copab 4257   cdm 4870  coprab 6074 This theorem is referenced by:  dmoprabss  6147  reldmoprab  6150  fnoprabg  6163  1st2val  6364  2nd2val  6365  linedegen  26069 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-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-dm 4880  df-oprab 6077
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