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Theorem iunxdif2 3675
 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 3672 . . 3
2 difss 3043 . . . . 5
3 iunss1 3638 . . . . 5
42, 3ax-mp 7 . . . 4
5 iunxdif2.1 . . . . 5
65cbviunv 3666 . . . 4
74, 6sseqtr4i 2951 . . 3
81, 7jctil 295 . 2
9 eqss 2933 . 2
108, 9sylibr 137 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1226  wral 2280  wrex 2281   cdif 2887   wss 2890  ciun 3627 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000 This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-ral 2285  df-rex 2286  df-v 2533  df-dif 2893  df-in 2897  df-ss 2904  df-iun 3629 This theorem is referenced by: (None)
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