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Theorem ssdisj 3669
 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 3649 . . . 4
2 ssrin 3558 . . . . 5
3 sstr2 3347 . . . . 5
42, 3syl 16 . . . 4
51, 4syl5bir 210 . . 3
65imp 419 . 2
7 ss0 3650 . 2
86, 7syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   cin 3311   wss 3312  c0 3620 This theorem is referenced by:  djudisj  5289  fimacnvdisj  5613  marypha1lem  7430  ackbij1lem16  8107  ackbij1lem18  8109  fin23lem20  8209  fin23lem30  8214  elcls3  17139  neindisj  17173  imadifxp  24030  diophren  26865 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-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-nul 3621
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