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Theorem ssrd 3508
 Description: Deduction rule based on subclass definition. (Contributed by Thierry Arnoux, 8-Mar-2017.)
Hypotheses
Ref Expression
ssrd.0
ssrd.1
ssrd.2
ssrd.3
Assertion
Ref Expression
ssrd

Proof of Theorem ssrd
StepHypRef Expression
1 ssrd.0 . . 3
2 ssrd.3 . . 3
31, 2alrimi 1877 . 2
4 ssrd.1 . . 3
5 ssrd.2 . . 3
64, 5dfss2f 3494 . 2
73, 6sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  A.wal 1393  F/wnf 1616  e.wcel 1818  F/_wnfc 2605  C_wss 3475 This theorem is referenced by:  eqrd  3521  neiptopnei  19633  rabss3d  27412  ssfiunibd  31509  stoweidlem52  31834  stoweidlem59  31841 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-or 370  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-in 3482  df-ss 3489
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