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Theorem intiin 4020
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 3928 . 2
2 df-iin 3972 . 2
31, 2eqtr4i 2376 1
Colors of variables: wff setvar class
Syntax hints:   wceq 1642   wcel 1710  cab 2339  wral 2614  cint 3926  ciin 3970
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-ral 2619  df-int 3927  df-iin 3972
This theorem is referenced by: (None)
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