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Theorem intun 4282
 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 1725 . . . 4
2 elun 3603 . . . . . . 7
32imbi1i 326 . . . . . 6
4 jaob 790 . . . . . 6
53, 4bitri 252 . . . . 5
65albii 1687 . . . 4
7 vex 3081 . . . . . 6
87elint 4255 . . . . 5
97elint 4255 . . . . 5
108, 9anbi12i 701 . . . 4
111, 6, 103bitr4i 280 . . 3
127elint 4255 . . 3
13 elin 3646 . . 3
1411, 12, 133bitr4i 280 . 2
1514eqriv 2416 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wo 369   wa 370  wal 1435   wceq 1437   wcel 1867   cun 3431   cin 3432  cint 4249 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-v 3080  df-un 3438  df-in 3440  df-int 4250 This theorem is referenced by:  intunsn  4289  riinint  5102  fiin  7933  elfiun  7941  elrfi  35274
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