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Theorem elinti 3812
 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 3811 . . 3
2 eleq2 2218 . . . 4
32rspccv 2810 . . 3
41, 3syl6bi 162 . 2
54pm2.43i 49 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 2125  wral 2432  cint 3803 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-v 2711  df-int 3804 This theorem is referenced by: (None)
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