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Theorem elint 4292
 Description: Membership in class intersection. (Contributed by NM, 21-May-1994.)
Hypothesis
Ref Expression
elint.1
Assertion
Ref Expression
elint
Distinct variable groups:   ,   ,

Proof of Theorem elint
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elint.1 . 2
2 eleq1 2529 . . . 4
32imbi2d 316 . . 3
43albidv 1713 . 2
5 df-int 4287 . 2
61, 4, 5elab2 3249 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  e.wcel 1818   cvv 3109  |^|cint 4286 This theorem is referenced by:  elint2  4293  elintab  4297  intss1  4301  intssOLD  4308  intun  4319  intpr  4320  cssmre  18724  dfom5b  29562 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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-int 4287
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