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Theorem dmoprabss 6158
 Description: The domain of an operation class abstraction. (Contributed by NM, 24-Aug-1995.)
Assertion
Ref Expression
dmoprabss
Distinct variable groups:   ,,,   ,,,
Allowed substitution hints:   (,,)

Proof of Theorem dmoprabss
StepHypRef Expression
1 dmoprab 6157 . 2
2 19.42v 1929 . . . 4
32opabbii 4275 . . 3
4 opabssxp 4953 . . 3
53, 4eqsstri 3380 . 2
61, 5eqsstri 3380 1
 Colors of variables: wff set class Syntax hints:   wa 360  wex 1551   wcel 1726   wss 3322  copab 4268   cxp 4879   cdm 4881  coprab 6085 This theorem is referenced by:  oprabexd  6189  oprabex  6190  elmpt2cl  6291  bropopvvv  6429  mpt2ndm0  6476  dmaddsr  8965  dmmulsr  8966  axaddf  9025  axmulf  9026  2wlkonot3v  28407  2spthonot3v  28408 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-xp 4887  df-dm 4891  df-oprab 6088
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