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Theorem iunxdif2 4014
 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 4011 . . 3
2 difss 3393 . . . . 5
3 iunss1 3980 . . . . 5
42, 3ax-mp 8 . . . 4
5 iunxdif2.1 . . . . 5
65cbviunv 4005 . . . 4
74, 6sseqtr4i 3304 . . 3
81, 7jctil 523 . 2
9 eqss 3287 . 2
108, 9sylibr 203 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358   wceq 1642  wral 2614  wrex 2615   cdif 3206   wss 3257  ciun 3969 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259  df-iun 3971 This theorem is referenced by: (None)
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