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Theorem elrnmpt2g 5613
 Description: Membership in the range of an operation class abstraction. (Contributed by NM, 27-Aug-2007.) (Revised by Mario Carneiro, 31-Aug-2015.)
Hypothesis
Ref Expression
rngop.1
Assertion
Ref Expression
elrnmpt2g
Distinct variable groups:   ,   ,,
Allowed substitution hints:   ()   (,)   (,)   (,)   (,)

Proof of Theorem elrnmpt2g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq1 2046 . . 3
212rexbidv 2349 . 2
3 rngop.1 . . 3
43rnmpt2 5611 . 2
52, 4elab2g 2689 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243   wcel 1393  wrex 2307   crn 4346   cmpt2 5514 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-cnv 4353  df-dm 4355  df-rn 4356  df-oprab 5516  df-mpt2 5517 This theorem is referenced by: (None)
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