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Theorem ssrd 2950
 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 1415 . 2
4 ssrd.1 . . 3
5 ssrd.2 . . 3
64, 5dfss2f 2936 . 2
73, 6sylibr 137 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1241  wnf 1349   wcel 1393  wnfc 2165   wss 2917 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-in 2924  df-ss 2931 This theorem is referenced by:  eqrd  2963
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