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Theorem elint 4048
 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 2495 . . . 4
32imbi2d 308 . . 3
43albidv 1635 . 2
5 df-int 4043 . 2
61, 4, 5elab2 3077 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549   wceq 1652   wcel 1725  cvv 2948  cint 4042 This theorem is referenced by:  elint2  4049  elintab  4053  intss1  4057  intss  4063  intun  4074  intpr  4075  cssmre  16910  dfom5b  25722 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-int 4043
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