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Theorem elint2 3933
 Description: Membership in class intersection. (Contributed by NM, 14-Oct-1999.)
Hypothesis
Ref Expression
elint2.1 A V
Assertion
Ref Expression
elint2 (A Bx B A x)
Distinct variable groups:   x,A   x,B

Proof of Theorem elint2
StepHypRef Expression
1 elint2.1 . . 3 A V
21elint 3932 . 2 (A Bx(x BA x))
3 df-ral 2619 . 2 (x B A xx(x BA x))
42, 3bitr4i 243 1 (A Bx B A x)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540   ∈ wcel 1710  ∀wral 2614  Vcvv 2859  ∩cint 3926 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-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861  df-int 3927 This theorem is referenced by:  elintg  3934  ssint  3942  intssuni  3948  iinuni  4049  dfint3  4318
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