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Theorem unidif 4039
 Description: If the difference contains the largest members of , then the union of the difference is the union of . (Contributed by NM, 22-Mar-2004.)
Assertion
Ref Expression
unidif
Distinct variable groups:   ,,   ,,

Proof of Theorem unidif
StepHypRef Expression
1 uniss2 4038 . . 3
2 difss 3466 . . . 4
32unissi 4030 . . 3
41, 3jctil 524 . 2
5 eqss 3355 . 2
64, 5sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652  wral 2697  wrex 2698   cdif 3309   wss 3312  cuni 4007 This theorem is referenced by:  ordunidif  4621 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-uni 4008
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