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Theorem ssrd 3097
 Description: Deduction 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 1502 . 2
4 ssrd.1 . . 3
5 ssrd.2 . . 3
64, 5dfss2f 3083 . 2
73, 6sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1329  wnf 1436   wcel 1480  wnfc 2266   wss 3066 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-in 3072  df-ss 3079 This theorem is referenced by:  eqrd  3110  exmidomni  7007
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