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Theorem iunxdif2 3861
 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 3858 . . 3
2 difss 3202 . . . . 5
3 iunss1 3824 . . . . 5
42, 3ax-mp 5 . . . 4
5 iunxdif2.1 . . . . 5
65cbviunv 3852 . . . 4
74, 6sseqtrri 3132 . . 3
81, 7jctil 310 . 2
9 eqss 3112 . 2
108, 9sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1331  wral 2416  wrex 2417   cdif 3068   wss 3071  ciun 3813 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-in1 603  ax-in2 604  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 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-dif 3073  df-in 3077  df-ss 3084  df-iun 3815 This theorem is referenced by: (None)
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