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Theorem intun 3797
 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 1457 . . . 4
2 elun 3212 . . . . . . 7
32imbi1i 237 . . . . . 6
4 jaob 699 . . . . . 6
53, 4bitri 183 . . . . 5
65albii 1446 . . . 4
7 vex 2684 . . . . . 6
87elint 3772 . . . . 5
97elint 3772 . . . . 5
108, 9anbi12i 455 . . . 4
111, 6, 103bitr4i 211 . . 3
127elint 3772 . . 3
13 elin 3254 . . 3
1411, 12, 133bitr4i 211 . 2
1514eqriv 2134 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wo 697  wal 1329   wceq 1331   wcel 1480   cun 3064   cin 3065  cint 3766 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-in 3072  df-int 3767 This theorem is referenced by:  intunsn  3804  riinint  4795
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