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Theorem iunxdif2 4131
 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 4128 . . 3
2 difss 3466 . . . . 5
3 iunss1 4096 . . . . 5
42, 3ax-mp 8 . . . 4
5 iunxdif2.1 . . . . 5
65cbviunv 4122 . . . 4
74, 6sseqtr4i 3373 . . 3
81, 7jctil 524 . 2
9 eqss 3355 . 2
108, 9sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652  wral 2697  wrex 2698   cdif 3309   wss 3312  ciun 4085 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-iun 4087
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