 New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  intiin GIF version

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 A = x A x
Distinct variable group:   x,A

Proof of Theorem intiin
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 dfint2 3928 . 2 A = {y x A y x}
2 df-iin 3972 . 2 x A x = {y x A y x}
31, 2eqtr4i 2376 1 A = x A x
 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)
 Copyright terms: Public domain W3C validator