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Theorem trsucss 4110
Description: A member of the successor of a transitive class is a subclass of it. (Contributed by NM, 4-Oct-2003.)
Assertion
Ref Expression
trsucss  Tr  suc 
C_

Proof of Theorem trsucss
StepHypRef Expression
1 elsuci 4089 . 2  suc
2 trss 3837 . . 3  Tr  C_
3 eqimss 2974 . . . 4  C_
43a1i 9 . . 3  Tr  C_
52, 4jaod 624 . 2  Tr  C_
61, 5syl5 28 1  Tr  suc 
C_
Colors of variables: wff set class
Syntax hints:   wi 4   wo 616   wceq 1228   wcel 1374    C_ wss 2894   Tr wtr 3828   suc csuc 4051
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ral 2289  df-v 2537  df-un 2899  df-in 2901  df-ss 2908  df-sn 3356  df-uni 3555  df-tr 3829  df-suc 4057
This theorem is referenced by:  onsucsssucr  4184  ordpwsucss  4227
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