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Theorem intun 4083
 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 1604 . . . 4
2 elun 3489 . . . . . . 7
32imbi1i 317 . . . . . 6
4 jaob 760 . . . . . 6
53, 4bitri 242 . . . . 5
65albii 1576 . . . 4
7 vex 2960 . . . . . 6
87elint 4057 . . . . 5
97elint 4057 . . . . 5
108, 9anbi12i 680 . . . 4
111, 6, 103bitr4i 270 . . 3
127elint 4057 . . 3
13 elin 3531 . . 3
1411, 12, 133bitr4i 270 . 2
1514eqriv 2434 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 359   wa 360  wal 1550   wceq 1653   wcel 1726   cun 3319   cin 3320  cint 4051 This theorem is referenced by:  intunsn  4090  riinint  5127  fiin  7428  elfiun  7436  elrfi  26749 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-v 2959  df-un 3326  df-in 3328  df-int 4052
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