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Theorem ssrd 3353
 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 1781 . 2
4 ssrd.1 . . 3
5 ssrd.2 . . 3
64, 5dfss2f 3339 . 2
73, 6sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549  wnf 1553   wcel 1725  wnfc 2559   wss 3320 This theorem is referenced by:  eqrd  3366  neiptopnei  17196  rabss3d  23995 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 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-in 3327  df-ss 3334
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