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Theorem trsucss 4968
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

Proof of Theorem trsucss
StepHypRef Expression
1 elsuci 4949 . 2
2 trss 4554 . . 3
3 eqimss 3555 . . . 4
43a1i 11 . . 3
52, 4jaod 380 . 2
61, 5syl5 32 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  \/wo 368  =wceq 1395  e.wcel 1818  C_wss 3475  Trwtr 4545  succsuc 4885
This theorem is referenced by:  efgmnvl  16732
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-un 3480  df-in 3482  df-ss 3489  df-sn 4030  df-uni 4250  df-tr 4546  df-suc 4889
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