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Theorem ssdisj 3876
 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 3815 . . . 4
2 ssrin 3722 . . . . 5
3 sstr2 3510 . . . . 5
42, 3syl 16 . . . 4
51, 4syl5bir 218 . . 3
65imp 429 . 2
7 ss0 3816 . 2
86, 7syl 16 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  i^icin 3474  C_wss 3475   c0 3784 This theorem is referenced by:  djudisj  5439  fimacnvdisj  5768  marypha1lem  7913  ackbij1lem16  8636  ackbij1lem18  8638  fin23lem20  8738  fin23lem30  8743  elcls3  19584  neindisj  19618  imadifxp  27458  diophren  30747 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785
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