Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfin4 Unicode version

Theorem dfin4 3316
 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 3296 . . 3
2 dfss4 3310 . . 3
31, 2mpbi 201 . 2
4 difin 3313 . . 3
54difeq2i 3208 . 2
63, 5eqtr3i 2275 1
 Colors of variables: wff set class Syntax hints:   wceq 1619   cdif 3075   cin 3077   wss 3078 This theorem is referenced by:  indif  3318  cnvin  4995  imain  5185  resin  5352  elcls  16642  cmmbl  18724  mbfeqalem  18829  itg1addlem4  18886  itg1addlem5  18887 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-rab 2516  df-v 2729  df-dif 3081  df-in 3085  df-ss 3089
 Copyright terms: Public domain W3C validator