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Theorem ssdisj 3837
 Description: Intersection with a subclass of a disjoint class. (Contributed by FL, 24-Jan-2007.)
Assertion
Ref Expression
ssdisj

Proof of Theorem ssdisj
StepHypRef Expression
1 ss0b 3776 . . . 4
2 ssrin 3684 . . . . 5
3 sstr2 3472 . . . . 5
42, 3syl 16 . . . 4
51, 4syl5bir 218 . . 3
65imp 429 . 2
7 ss0 3777 . 2
86, 7syl 16 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1370   cin 3436   wss 3437  c0 3746 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-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-v 3080  df-dif 3440  df-in 3444  df-ss 3451  df-nul 3747 This theorem is referenced by:  djudisj  5374  fimacnvdisj  5698  marypha1lem  7795  ackbij1lem16  8516  ackbij1lem18  8518  fin23lem20  8618  fin23lem30  8623  elcls3  18820  neindisj  18854  imadifxp  26091  diophren  29301
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