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Theorem dfint2 3928
 Description: Alternate definition of class intersection. (Contributed by NM, 28-Jun-1998.)
Assertion
Ref Expression
dfint2 A = {x y A x y}
Distinct variable group:   x,y,A

Proof of Theorem dfint2
StepHypRef Expression
1 df-int 3927 . 2 A = {x y(y Ax y)}
2 df-ral 2619 . . 3 (y A x yy(y Ax y))
32abbii 2465 . 2 {x y A x y} = {x y(y Ax y)}
41, 3eqtr4i 2376 1 A = {x y A x y}
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540   = wceq 1642   ∈ wcel 1710  {cab 2339  ∀wral 2614  ∩cint 3926 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 This theorem is referenced by:  inteq  3929  nfint  3936  intiin  4020
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