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Theorem intun 4319
 Description: The class intersection of the union of two classes. Theorem 78 of [Suppes] p. 42. (Contributed by NM, 22-Sep-2002.)
Assertion
Ref Expression
intun

Proof of Theorem intun
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 19.26 1680 . . . 4
2 elun 3644 . . . . . . 7
32imbi1i 325 . . . . . 6
4 jaob 783 . . . . . 6
53, 4bitri 249 . . . . 5
65albii 1640 . . . 4
7 vex 3112 . . . . . 6
87elint 4292 . . . . 5
97elint 4292 . . . . 5
108, 9anbi12i 697 . . . 4
111, 6, 103bitr4i 277 . . 3
127elint 4292 . . 3
13 elin 3686 . . 3
1411, 12, 133bitr4i 277 . 2
1514eqriv 2453 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  \/wo 368  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  u.cun 3473  i^icin 3474  |^|cint 4286 This theorem is referenced by:  intunsn  4326  riinint  5264  fiin  7902  elfiun  7910  elrfi  30626 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-or 370  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-v 3111  df-un 3480  df-in 3482  df-int 4287
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