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Theorem elrnmpt2g 6197
 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 2444 . . 3
212rexbidv 2753 . 2
3 rngop.1 . . 3
43rnmpt2 6195 . 2
52, 4elab2g 3103 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wceq 1369   wcel 1756  wrex 2711   crn 4836   cmpt2 6088 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-9 1760  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2419  ax-sep 4408  ax-nul 4416  ax-pr 4526 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-eu 2256  df-mo 2257  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-rex 2716  df-rab 2719  df-v 2969  df-dif 3326  df-un 3328  df-in 3330  df-ss 3337  df-nul 3633  df-if 3787  df-sn 3873  df-pr 3875  df-op 3879  df-br 4288  df-opab 4346  df-cnv 4843  df-dm 4845  df-rn 4846  df-oprab 6090  df-mpt2 6091 This theorem is referenced by:  ordtbas2  18770  txopn  19150  tgisline  23005  elsx  26560
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