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Theorem elrnmpt2g 6414
 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:   ,   ,,

Proof of Theorem elrnmpt2g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq1 2461 . . 3
212rexbidv 2975 . 2
3 rngop.1 . . 3
43rnmpt2 6412 . 2
52, 4elab2g 3248 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  E.wrex 2808  rancrn 5005  e.cmpt2 6298 This theorem is referenced by:  ordtbas2  19692  txopn  20103  tgisline  24007  elsx  28165 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-cnv 5012  df-dm 5014  df-rn 5015  df-oprab 6300  df-mpt2 6301
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