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Theorem iundif2 4397
 Description: Indexed union of class difference. Generalization of half of theorem "De Morgan's laws" in [Enderton] p. 31. Use intiin 4384 to recover Enderton's theorem. (Contributed by NM, 19-Aug-2004.)
Assertion
Ref Expression
iundif2
Distinct variable group:   ,

Proof of Theorem iundif2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eldif 3485 . . . . 5
21rexbii 2959 . . . 4
3 r19.42v 3012 . . . 4
4 rexnal 2905 . . . . . 6
5 vex 3112 . . . . . . 7
6 eliin 4336 . . . . . . 7
75, 6ax-mp 5 . . . . . 6
84, 7xchbinxr 311 . . . . 5
98anbi2i 694 . . . 4
102, 3, 93bitri 271 . . 3
11 eliun 4335 . . 3
12 eldif 3485 . . 3
1310, 11, 123bitr4i 277 . 2
1413eqriv 2453 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  E.wrex 2808   cvv 3109  \cdif 3472  U_ciun 4330  |^|_ciin 4331 This theorem is referenced by:  iuncld  19546  pnrmopn  19844  alexsublem  20544  bcth3  21770  iundifdifd  27429  iundifdif  27430 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-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-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-iun 4332  df-iin 4333
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