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Theorem dfin4 3737
Description: Alternate definition of the intersection of two classes. Exercise 4.10(q) of [Mendelson] p. 231. (Contributed by NM, 25-Nov-2003.)
Assertion
Ref Expression
dfin4

Proof of Theorem dfin4
StepHypRef Expression
1 inss1 3717 . . 3
2 dfss4 3731 . . 3
31, 2mpbi 208 . 2
4 difin 3734 . . 3
54difeq2i 3618 . 2
63, 5eqtr3i 2488 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  \cdif 3472  i^icin 3474  C_wss 3475
This theorem is referenced by:  indif  3739  cnvin  5418  imain  5669  resin  5842  elcls  19574  cmmbl  21945  mbfeqalem  22049  itg1addlem4  22106  itg1addlem5  22107  inelsiga  28135  mblfinlem4  30054  ismblfin  30055  cnambfre  30063  stoweidlem50  31832
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489
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