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Theorem intiin 3972
 Description: Class intersection in terms of indexed intersection. Definition in [Stoll] p. 44. (Contributed by NM, 28-Jun-1998.)
Assertion
Ref Expression
intiin
Distinct variable group:   ,

Proof of Theorem intiin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfint2 3880 . 2
2 df-iin 3924 . 2
31, 2eqtr4i 2319 1
 Colors of variables: wff set class Syntax hints:   wceq 1632   wcel 1696  cab 2282  wral 2556  cint 3878  ciin 3922 This theorem is referenced by:  relint  4825  intpreima  5672  ixpint  6859  firest  13353  efger  15043  rintopn  16671  intcld  16793  iundifdifd  23175  iundifdif  23176  inttop3  25619 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-ral 2561  df-int 3879  df-iin 3924
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