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Theorem iunxdif2 4326
 Description: Indexed union with a class difference as its index. (Contributed by NM, 10-Dec-2004.)
Hypothesis
Ref Expression
iunxdif2.1
Assertion
Ref Expression
iunxdif2
Distinct variable groups:   ,,   ,,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem iunxdif2
StepHypRef Expression
1 iunss2 4323 . . 3
2 difss 3560 . . . . 5
3 iunss1 4290 . . . . 5
42, 3ax-mp 5 . . . 4
5 iunxdif2.1 . . . . 5
65cbviunv 4317 . . . 4
74, 6sseqtr4i 3465 . . 3
81, 7jctil 540 . 2
9 eqss 3447 . 2
108, 9sylibr 216 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371   wceq 1444  wral 2737  wrex 2738   cdif 3401   wss 3404  ciun 4278 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ral 2742  df-rex 2743  df-v 3047  df-dif 3407  df-in 3411  df-ss 3418  df-iun 4280 This theorem is referenced by: (None)
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