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Theorem sylan9ss 2958
 Description: A subclass transitivity deduction. (Contributed by NM, 27-Sep-2004.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Hypotheses
Ref Expression
sylan9ss.1
sylan9ss.2
Assertion
Ref Expression
sylan9ss

Proof of Theorem sylan9ss
StepHypRef Expression
1 sylan9ss.1 . 2
2 sylan9ss.2 . 2
3 sstr 2953 . 2
41, 2, 3syl2an 273 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   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-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  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-in 2924  df-ss 2931 This theorem is referenced by:  sylan9ssr  2959  psstr  3049  sspsstr  3050  psssstr  3051  unss12  3115  ss2in  3164  relrelss  4844  funssxp  5060
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