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Theorem difabs 3728
Description: Absorption-like law for class difference: you can remove a class only once. (Contributed by FL, 2-Aug-2009.)
Assertion
Ref Expression
difabs

Proof of Theorem difabs
StepHypRef Expression
1 difun1 3724 . 2
2 unidm 3613 . . 3
32difeq2i 3585 . 2
41, 3eqtr3i 2485 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1370  \cdif 3439  u.cun 3440
This theorem is referenced by:  axcclem  8763  lpdifsn  19146  bwthOLD  19413  compne  30156
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ral 2805  df-rab 2809  df-v 3083  df-dif 3445  df-un 3447  df-in 3449
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