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Theorem elrn2 5111
 Description: Membership in a range. (Contributed by NM, 10-Jul-1994.)
Hypothesis
Ref Expression
elrn.1
Assertion
Ref Expression
elrn2
Distinct variable groups:   ,   ,

Proof of Theorem elrn2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elrn.1 . 2
2 opeq2 3987 . . . 4
32eleq1d 2504 . . 3
43exbidv 1637 . 2
5 dfrn3 5062 . 2
61, 4, 5elab2 3087 1
 Colors of variables: wff set class Syntax hints:   wb 178  wex 1551   wceq 1653   wcel 1726  cvv 2958  cop 3819   crn 4881 This theorem is referenced by:  elrn  5112  dmrnssfld  5131  rniun  5284  ssrnres  5311  relssdmrn  5392  fvelrn  5868  tz7.48-1  6702  dfrn5  25403 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 4332  ax-nul 4340  ax-pr 4405 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 4215  df-opab 4269  df-cnv 4888  df-dm 4890  df-rn 4891
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