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Theorem elinti 3935
Description: Membership in class intersection. (Contributed by NM, 14-Oct-1999.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
elinti

Proof of Theorem elinti
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elintg 3934 . . 3
2 eleq2 2414 . . . 4
32rspccv 2952 . . 3
41, 3syl6bi 219 . 2
54pm2.43i 43 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wcel 1710  wral 2614  cint 3926
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861  df-int 3927
This theorem is referenced by: (None)
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